{
  "id": 6397,
  "curve_key": "1944535065181886965246144:-391154879073379329057222420633321472",
  "ainvs": [
    "0",
    "1",
    "0",
    "-40511147191289311775961",
    "452725554469574211419133216252135"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 167.78119541794516,
  "faltings_height": 12.04873036120235,
  "conductor": "2390681677049094299819723099307840",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "29",
    "31",
    "59",
    "83",
    "103",
    "113",
    "149",
    "163",
    "173",
    "463",
    "2437",
    "4217"
  ],
  "discriminant": "4166496624233158840971977128041063799434250446329887599722885304422400",
  "regulator": "75578663.16930944786094799939314904176017549212337387099308",
  "points": [
    [
      "621677286327",
      "-464257848110612160"
    ],
    [
      "-176827028913",
      "45685878583380360"
    ],
    [
      "-152260488966",
      "55597469941290339"
    ],
    [
      "301427054277",
      "-125014839870272040"
    ],
    [
      "-31305181503",
      "41112709006673700"
    ],
    [
      "532308942867",
      "360165954412426800"
    ],
    [
      "1079613042987",
      "-1102304317222556760"
    ],
    [
      "248562725409",
      "75764251220694036"
    ],
    [
      "-191642719156653/961",
      "730243438563114113040/29791"
    ],
    [
      "732092990947/81",
      "6812021401736559040/729"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Z/2xZ/2 X400a family y^2=x(x+A)(x+B), A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q), at T=p/q=-110/59. Family equations as posted by wgxli with curve #4252; section formulas from the Layr Labs Elliptic Rank Challenge repository (submission/research/x400a-family.gp, commit 7482bf9). T selected by our Mestre-Nagao sieve; PARI/GP 2.19 ellrank seeded with the family sections, bounds [10,10]; torsion Z/2xZ/2 (elltors).",
  "created_at": "2026-11-02 01:17:50",
  "updated_at": "2026-11-02 01:17:50"
}