{
  "id": 6386,
  "curve_key": "1957712219228148940787566932288:-2730824197096661848154466025231133701419609600",
  "ainvs": [
    "0",
    "0",
    "0",
    "-40785671233919769599740977756",
    "3160676154047062324252854195869367709976400"
  ],
  "rank_lower_bound": 11,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 209.24798803868003,
  "faltings_height": 15.25328550661266,
  "conductor": "78003799986552116346057223715901286275648",
  "bad_primes": [
    "2",
    "3",
    "11",
    "19",
    "29",
    "103",
    "163",
    "311",
    "379",
    "421",
    "449",
    "487",
    "521",
    "997",
    "1061",
    "2549",
    "7937"
  ],
  "discriminant": "26504486290561873733865010930732184224590988989833950267482790707301416644130343501824",
  "regulator": "20135308275.1584907281067611794804946661882665846767919959023",
  "points": [
    [
      "138573433640334",
      "412110884542545326160"
    ],
    [
      "-98477561315859",
      "2494419960069303066405"
    ],
    [
      "231380042877852",
      "2472046792807666661136"
    ],
    [
      "2535632489869941/25",
      "32439500651776002925239/125"
    ],
    [
      "-64633057681962",
      "2350910160490102268112"
    ],
    [
      "6663496566287566566/85849",
      "-17107689943419947041782989520/25153757"
    ],
    [
      "960308742980950/9",
      "4148377132665721266080/27"
    ],
    [
      "-74448250941508156383/334084",
      "210056306635347003577403925201/193100552"
    ],
    [
      "27202390075103782",
      "4486406911837403541449824"
    ],
    [
      "1027912629489142342/19881",
      "3058130845182957925378065904/2803221"
    ],
    [
      "25005617536145884/225",
      "-81535041444229212698848/3375"
    ]
  ],
  "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=-19/311. 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 [11,11]; torsion Z/2xZ/2 (elltors).",
  "created_at": "2026-11-02 01:04:56",
  "updated_at": "2026-11-02 01:04:56"
}