{
  "id": 6390,
  "curve_key": "7770858358813955945910601:-14872200255990229858007297360704545349",
  "ainvs": [
    "1",
    "0",
    "1",
    "-161892882475290748873138",
    "17213194740715941632487356975446388"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 171.93726858307505,
  "faltings_height": 12.358577715930515,
  "conductor": "12345789526483387306160243584290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "31",
    "47",
    "67",
    "149",
    "331",
    "379",
    "569",
    "631",
    "1021",
    "2083",
    "2441"
  ],
  "discriminant": "143559360273849647413620068052124780811330737697721295868810579972010000",
  "regulator": "102800215.9574029569857393092999858918072405217651346922124",
  "points": [
    [
      "-431468598023",
      "82100599625482757"
    ],
    [
      "1111882732498",
      "1100821522688232488"
    ],
    [
      "-44455317654719/169",
      "448087737657935606165/2197"
    ],
    [
      "-37846743848",
      "152597864341496915"
    ],
    [
      "-240831450971",
      "-205508807572418515"
    ],
    [
      "937812297454",
      "830774099160069185"
    ],
    [
      "647324888209",
      "-428560860794498575"
    ],
    [
      "18366456146464",
      "78692684672426885540"
    ],
    [
      "-3135239480003543/8281",
      "117316351364582219537267/753571"
    ],
    [
      "-1616624032181684/7225",
      "126209767256643795254156/614125"
    ]
  ],
  "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=192/379. 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 01:11:13",
  "updated_at": "2026-11-02 01:11:13"
}