{
  "id": 4603,
  "curve_key": "13779701088004852685671804561:-1617446586062227597601705004914711405488441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-287077106000101097618162595",
    "1872044659794220981539436339856114465025"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 194.37898225338807,
  "faltings_height": 13.882181851942626,
  "conductor": "2889000441526096910007811045669530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "23",
    "31",
    "43",
    "47",
    "67",
    "79",
    "109",
    "1272918873742049461"
  ],
  "discriminant": "207417342466629804899506932143657533855438663218711452803685924298432000000000",
  "regulator": "81958694320.29007713465428635079100771450181598292096239128",
  "points": [
    [
      "2436620372367049710/113569",
      "2861225865928978803735443865/38272753"
    ],
    [
      "1918123948757170477422/26306641",
      "-81915635521696199926248275871231/134926761689"
    ],
    [
      "16243303107928421484782/1633857241",
      "-52080517227954253338269862538043/66042143538461"
    ],
    [
      "130862110145735128633942590/13084287762841",
      "53810293217729788430456994316169176005/47328760465791484861"
    ],
    [
      "4375360860207390/121",
      "262082667717614008229355/1331"
    ],
    [
      "77695022367723353310/3052009",
      "560773009992183933595700219715/5331859723"
    ],
    [
      "195857538644245754/15625",
      "-30451774495652721090159383/1953125"
    ],
    [
      "46030238964033242345090910/4418921107129",
      "-32094129968902829398307625040928478165/9289115694481334867"
    ],
    [
      "74016844610810670",
      "-20137049597830148069870295"
    ],
    [
      "1892053383193710/169",
      "-17203443511131493004115/2197"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 277/377 for y^2 + (7t^2+309) x y - 91 (t^2-1)(t^2-25)(t^2-121) y = x^3 from https://github.com/Layr-Labs/elliptic-rank-challenge-public/blob/main/submission/board/3-r12-z3k3.ec",
  "created_at": "2026-10-18 23:10:05",
  "updated_at": "2026-10-18 23:10:05"
}