{
  "name": "bsd_conjecture_dataset_006",
  "created": "2026-01-08T08:11:12.247Z",
  "sample_count": 97,
  "parameters_range": {
    "a": {
      "min": -5.2,
      "max": -2,
      "mean": -3.649484536082472
    },
    "b": {
      "min": -5.4,
      "max": 5.2,
      "mean": 0.06391752577319154
    },
    "rank": {
      "min": 3,
      "max": 9,
      "mode": {
        "3": 47,
        "9": 50
      }
    }
  },
  "samples": [
    {
      "id": "bsd_000550",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
        "l_function_order": 9,
        "sha_group_size": 3
      },
      "image_file": "bsd_000550.jpg"
    },
    {
      "id": "bsd_000551",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
        "l_function_order": 9,
        "sha_group_size": 4
      },
      "image_file": "bsd_000551.jpg"
    },
    {
      "id": "bsd_000552",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
        "l_function_order": 9,
        "sha_group_size": 3
      },
      "image_file": "bsd_000552.jpg"
    },
    {
      "id": "bsd_000553",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
        "l_function_order": 9,
        "sha_group_size": 4
      },
      "image_file": "bsd_000553.jpg"
    },
    {
      "id": "bsd_000554",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
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        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
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      "bsd_conjecture": {
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        "sha_group_size": 4
      },
      "image_file": "bsd_000554.jpg"
    },
    {
      "id": "bsd_000555",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
        "l_function_order": 9,
        "sha_group_size": 5
      },
      "image_file": "bsd_000555.jpg"
    },
    {
      "id": "bsd_000556",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
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      "bsd_conjecture": {
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        "sha_group_size": 4
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      "image_file": "bsd_000556.jpg"
    },
    {
      "id": "bsd_000557",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
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      "bsd_conjecture": {
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        "sha_group_size": 1
      },
      "image_file": "bsd_000557.jpg"
    },
    {
      "id": "bsd_000558",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
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      "bsd_conjecture": {
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        "sha_group_size": 4
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      "image_file": "bsd_000558.jpg"
    },
    {
      "id": "bsd_000559",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
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      "bsd_conjecture": {
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        "sha_group_size": 3
      },
      "image_file": "bsd_000559.jpg"
    },
    {
      "id": "bsd_000560",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
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      "bsd_conjecture": {
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        "sha_group_size": 2
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      "image_file": "bsd_000560.jpg"
    },
    {
      "id": "bsd_000561",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
        "rank": 9
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      "bsd_conjecture": {
        "l_function_order": 9,
        "sha_group_size": 4
      },
      "image_file": "bsd_000561.jpg"
    },
    {
      "id": "bsd_000562",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
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        "sha_group_size": 5
      },
      "image_file": "bsd_000562.jpg"
    },
    {
      "id": "bsd_000563",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
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      "bsd_conjecture": {
        "l_function_order": 9,
        "sha_group_size": 3
      },
      "image_file": "bsd_000563.jpg"
    },
    {
      "id": "bsd_000564",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
        "l_function_order": 9,
        "sha_group_size": 2
      },
      "image_file": "bsd_000564.jpg"
    },
    {
      "id": "bsd_000565",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
        "l_function_order": 9,
        "sha_group_size": 2
      },
      "image_file": "bsd_000565.jpg"
    },
    {
      "id": "bsd_000566",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
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        "sha_group_size": 2
      },
      "image_file": "bsd_000566.jpg"
    },
    {
      "id": "bsd_000567",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
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        "sha_group_size": 2
      },
      "image_file": "bsd_000567.jpg"
    },
    {
      "id": "bsd_000568",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
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        "sha_group_size": 4
      },
      "image_file": "bsd_000568.jpg"
    },
    {
      "id": "bsd_000569",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
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        "sha_group_size": 2
      },
      "image_file": "bsd_000569.jpg"
    },
    {
      "id": "bsd_000570",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
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        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
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        "sha_group_size": 2
      },
      "image_file": "bsd_000570.jpg"
    },
    {
      "id": "bsd_000571",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
        "rank": 9
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      "bsd_conjecture": {
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        "sha_group_size": 2
      },
      "image_file": "bsd_000571.jpg"
    },
    {
      "id": "bsd_000572",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
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        "sha_group_size": 3
      },
      "image_file": "bsd_000572.jpg"
    },
    {
      "id": "bsd_000573",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
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        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
        "rank": 9
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      "bsd_conjecture": {
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        "sha_group_size": 2
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      "image_file": "bsd_000573.jpg"
    },
    {
      "id": "bsd_000574",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
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        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
        "rank": 9
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      "bsd_conjecture": {
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        "sha_group_size": 1
      },
      "image_file": "bsd_000574.jpg"
    },
    {
      "id": "bsd_000575",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
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        "conductor": 2682,
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      "bsd_conjecture": {
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        "sha_group_size": 3
      },
      "image_file": "bsd_000575.jpg"
    },
    {
      "id": "bsd_000576",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
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        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
        "rank": 9
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      "bsd_conjecture": {
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        "sha_group_size": 4
      },
      "image_file": "bsd_000576.jpg"
    },
    {
      "id": "bsd_000577",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
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        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
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      "bsd_conjecture": {
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        "sha_group_size": 4
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      "image_file": "bsd_000577.jpg"
    },
    {
      "id": "bsd_000578",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
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        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
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      "bsd_conjecture": {
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        "sha_group_size": 1
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      "image_file": "bsd_000578.jpg"
    },
    {
      "id": "bsd_000579",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
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        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
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      "bsd_conjecture": {
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        "sha_group_size": 5
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      "image_file": "bsd_000579.jpg"
    },
    {
      "id": "bsd_000580",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
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        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
        "rank": 9
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      "bsd_conjecture": {
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        "sha_group_size": 3
      },
      "image_file": "bsd_000580.jpg"
    },
    {
      "id": "bsd_000581",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
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        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
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      "bsd_conjecture": {
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        "sha_group_size": 4
      },
      "image_file": "bsd_000581.jpg"
    },
    {
      "id": "bsd_000582",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
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        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
        "rank": 9
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      "bsd_conjecture": {
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        "sha_group_size": 1
      },
      "image_file": "bsd_000582.jpg"
    },
    {
      "id": "bsd_000583",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
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        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
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      "bsd_conjecture": {
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        "sha_group_size": 1
      },
      "image_file": "bsd_000583.jpg"
    },
    {
      "id": "bsd_000584",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
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        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
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        "sha_group_size": 1
      },
      "image_file": "bsd_000584.jpg"
    },
    {
      "id": "bsd_000585",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
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        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
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      "bsd_conjecture": {
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        "sha_group_size": 1
      },
      "image_file": "bsd_000585.jpg"
    },
    {
      "id": "bsd_000586",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
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        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
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        "sha_group_size": 5
      },
      "image_file": "bsd_000586.jpg"
    },
    {
      "id": "bsd_000587",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
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        "discriminant": -2682.3679999999986,
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        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
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        "sha_group_size": 5
      },
      "image_file": "bsd_000587.jpg"
    },
    {
      "id": "bsd_000588",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
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        "sha_group_size": 5
      },
      "image_file": "bsd_000588.jpg"
    },
    {
      "id": "bsd_000589",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
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        "sha_group_size": 1
      },
      "image_file": "bsd_000589.jpg"
    },
    {
      "id": "bsd_000590",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
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        "sha_group_size": 2
      },
      "image_file": "bsd_000590.jpg"
    },
    {
      "id": "bsd_000591",
      "elliptic_curve": {
        "equation": "y² = x³ + -5.20x + 5.20",
        "parameter_a": -5.2,
        "parameter_b": 5.2,
        "discriminant": -2682.3679999999986,
        "j_invariant": -5797.161290322585,
        "conductor": 2682,
        "rank": 9
      },
      "bsd_conjecture": {
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        "sha_group_size": 1
      },
      "image_file": "bsd_000591.jpg"
    },
    {
      "id": "bsd_000592",
      "elliptic_curve": {
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  ]
}