{
  "id": 5029,
  "curve_key": "1896662208:0",
  "ainvs": [
    "0",
    "0",
    "0",
    "-39513796",
    "0"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2,
    2
  ],
  "family": "congruent",
  "families": [
    "quartic",
    "congruent"
  ],
  "naive_height": 64.09008433686876,
  "faltings_height": 3.4090807730472195,
  "conductor": "632220736",
  "bad_primes": [
    "2",
    "7",
    "449"
  ],
  "discriminant": "3948446283755858136469504",
  "regulator": "261.15443343372725192061560195907582161409807",
  "points": [
    [
      "-14",
      "23520"
    ],
    [
      "7168",
      "291648"
    ],
    [
      "45486",
      "9607920"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Congruent-number curve y^2 = x^3 - n^2 x with n = 6286. Found in an exhaustive ellrank scan of squarefree n <= 20000; one of the smallest n of rank 3.",
  "created_at": "2026-10-21 01:48:24",
  "updated_at": "2026-10-21 01:48:24"
}