{
  "id": 4637,
  "curve_key": "67475487823566960348936353281:-17525629684850617156739226523908613073752321",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1405739329657645007269507360",
    "20284293616725134193874411080402881561600"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 199.1446856982319,
  "faltings_height": 14.292432348503706,
  "conductor": "3993916479095036308148774870430",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29",
    "41",
    "71",
    "331",
    "887755717",
    "5361446437"
  ],
  "discriminant": "37181709844539827546864677898707222311927850719440819047097468658319884288000000",
  "regulator": "93901953813.85403100073069416530019163953718833010792539710",
  "points": [
    [
      "761806290754917440/10201",
      "-593470490684663978255134880/1030301"
    ],
    [
      "1009439306729308758080/42680089",
      "4555143148775749356330591165280/278829021437"
    ],
    [
      "86880711206641175592205225280/3862461284582209",
      "-1611443982545108958414482197745179484055520/240046959224498186224927"
    ],
    [
      "6426442537029041077280/285035689",
      "34412394181268097665033655602080/4812257537387"
    ],
    [
      "13236661497939512350880/1682209",
      "-1522869803937516015199334412023680/2181825073"
    ],
    [
      "30888892804746428333120/279591841",
      "5149836138508027711728485144854240/4675055173361"
    ],
    [
      "78632150414449501375113680/2464639386889",
      "-344121400615061121334834794395369144480/3869279272346618213"
    ],
    [
      "1053806213376974496131648/48181567009",
      "-11456540726823621537198093864179936/10575998503176527"
    ],
    [
      "1760019215753690432/78961",
      "-110931337709568094094029088/22188041"
    ],
    [
      "61951476670692364719680/2836308049",
      "-91930456797420940955507816526880/151053257765593"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 319/461 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": "2026-10-19 09:07:34",
  "updated_at": "2026-10-19 09:07:34"
}