{
  "id": 6083,
  "curve_key": "18920690890461795260024988508225:-79626035151969488759930403791499184613343066625",
  "ainvs": [
    "1",
    "0",
    "0",
    "-394181060217954067917187260588",
    "92159762907372060623719986225470248351690167"
  ],
  "rank_lower_bound": 12,
  "torsion": [
    2,
    2
  ],
  "family": null,
  "families": [],
  "naive_height": 216.05342660756276,
  "faltings_height": 15.923214792006556,
  "conductor": "4128396631990771588539528525089728239975",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "43",
    "47",
    "59",
    "97",
    "107",
    "139",
    "257",
    "263",
    "463",
    "719",
    "953",
    "1409",
    "1831",
    "6829"
  ],
  "discriminant": "250671752190444715261009787462482561212827747286557989963140556549797013673299684766015625",
  "regulator": "24927168014.084435347376963484702691000444373870624336143132338",
  "points": [
    [
      "202588408910106",
      "4540693174288439525055"
    ],
    [
      "139039144488582",
      "-6327800168454628534791"
    ],
    [
      "-11464016697595563/16",
      "166376384670918425006751/64"
    ],
    [
      "2731780310056853137317/8994001",
      "18182288391606089787856419261621/26973008999"
    ],
    [
      "11008241374107",
      "-9371331642216810656241"
    ],
    [
      "-533399027949297/4",
      "95449242362537883568797/8"
    ],
    [
      "1057058866472982",
      "-29268015283907533630491"
    ],
    [
      "146195129738385704523/218089",
      "-1157444798086815586738366437558/101847563"
    ],
    [
      "-729621108047975895603/8473921",
      "-276300284624670099753085239192771/24667584031"
    ],
    [
      "1444422197726592618/5329",
      "889703324326134040692360843/389017"
    ],
    [
      "423650327359107",
      "1096092369624693207759"
    ],
    [
      "26383703446190215098/1369",
      "-135449017300421513559398655513/50653"
    ]
  ],
  "submitter": "The Wren",
  "history": [],
  "commentary": "Original specialization/search by kaankolcu (2026), public Yukon elliptic-rank challenge submission 43af8780-369f-484f-b8df-47147017654b. Source: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/f1c42abe0153e017898256f2d1ad9dbe7b47cd32/submission/board/2x2-12-own.ec . Specialization T=771/1409 of 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 twelve supplied points have been checked exactly on the minimal model and certified independent modulo torsion by an exact rank-12 F_5 reduction matrix at twelve good primes.",
  "created_at": "2026-10-29 00:53:25",
  "updated_at": "2026-10-29 00:53:25"
}