{
  "id": 6401,
  "curve_key": "8782695660841219021722048:-12072610379334232379336729184638530560",
  "ainvs": [
    "0",
    "0",
    "0",
    "-182972826267525396285876",
    "13972928679784991179787881000739040"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 172.3044768457713,
  "faltings_height": 12.412368571921036,
  "conductor": "454308257228250524769691706722752",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "17",
    "37",
    "59",
    "79",
    "109",
    "127",
    "379",
    "431",
    "433",
    "569",
    "8297"
  ],
  "discriminant": "307703607982562298104841560119769919173006308028403545840148291256356864",
  "regulator": "202468013.6214289513814171659961108068892791566795767181371",
  "points": [
    [
      "-183264349422",
      "-203347586342439792"
    ],
    [
      "74420729812",
      "27715204022909084"
    ],
    [
      "3225718091629",
      "5743533807012616615"
    ],
    [
      "-19649929895444838/96721",
      "6220175835797496727582824/30080231"
    ],
    [
      "390195010460310/529",
      "6441835998473046087840/12167"
    ],
    [
      "-5535434614743/16",
      "12120527885028796629/64"
    ],
    [
      "799266530181",
      "615078776590120485"
    ],
    [
      "-36943204512962/289",
      "922724875122407633672/4913"
    ],
    [
      "76502688702",
      "-20561124542283864"
    ],
    [
      "-218337266763",
      "208600873037192691"
    ]
  ],
  "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=242/629. 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 01:36:59",
  "updated_at": "2026-11-02 01:36:59"
}