{
  "id": 6114,
  "curve_key": "81707952228841579682207035732092736:-23236715369130206484497969271725382986766222646422016",
  "ainvs": [
    "0",
    "1",
    "0",
    "-1702249004767532910045979911085265",
    "26894346492048849530382240623467482515652787330863"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 241.16537820130534,
  "faltings_height": 17.933799347382074,
  "conductor": "1168567951348072752505784451372058351517634240",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "37",
    "53",
    "127",
    "227",
    "347",
    "359",
    "389",
    "967",
    "1093",
    "1231",
    "1663",
    "1693",
    "2591",
    "2909"
  ],
  "discriminant": "3213442194715285669595158458119447975911095385592443576091302995288069715239685890820329617909760000",
  "regulator": "183178615511610.03469215829450688795152662574000463579961821391",
  "points": [
    [
      "18342206458351453",
      "1357325399018538482865948"
    ],
    [
      "26265201061133503",
      "551150065526707961854848"
    ],
    [
      "170120556633385981",
      "68269806447865640026336620"
    ],
    [
      "-94567339374944243/4",
      "58746563657987802790750029/8"
    ],
    [
      "325335549534897937/16",
      "53108038576560164183952735/64"
    ],
    [
      "1414322453158389260689/1849",
      "53113272034214575612662083330760/79507"
    ],
    [
      "4782660915105953274682/157609",
      "111614054762001767284691240276691/62570773"
    ],
    [
      "10459330282967672468551/14371681",
      "275965512444277407500974878181914000/54483042671"
    ],
    [
      "16896948717118324578367/1229881",
      "3368921289028856556556383422439840/1363938029"
    ],
    [
      "1517106092922392186836951/70543201",
      "285664467021976875214046696527335840/592492345199"
    ],
    [
      "6580557020464564729423999/203433169",
      "6914027328376216720451895101898212400/2901567289447"
    ],
    [
      "266276723025416916775503572653111/38029286570521",
      "4345025031084333409246383651809519635479622326960/234518586100936627069"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Source parameter/search by bufferhe4d (2026), public Yukon submission 15009775-297e-4a19-9179-4a455b778310: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/6837b3bcd53a73fb5af3e271d91dec3148236631/submission/search/x400a-opus/xlog.txt . The source log records rank12 at T=20316/20767 in the rank-five X400a family posted by wgxli with curve#4252: y^2=x(x+A)(x+B), A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q). The published section code credits 0xArion submission7e9f6673-cf5f-4cb9-82b4-a22add86d720. Using its four selected sections, a local seeded PARI/GP replay recovered the twelve displayed points and bounds[12,12]. Every coordinate was checked exactly on the minimal model; independence modulo torsion was separately certified by an exact rank-12 F_5 reduction matrix at twelve good primes.",
  "created_at": "2026-10-29 02:49:46",
  "updated_at": "2026-10-29 02:49:46"
}