{
  "id": 4638,
  "curve_key": "1017151231672407573528551521:-32623921109752960396513642747669017265681",
  "ainvs": [
    "1",
    "0",
    "0",
    "-21190650659841824448511490",
    "37759167951101197534335803398505468100"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    3
  ],
  "family": null,
  "families": [],
  "naive_height": 186.57172884486195,
  "faltings_height": 13.388409116279032,
  "conductor": "1478729832407875338015623909010",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "23",
    "29",
    "37",
    "113",
    "313",
    "433",
    "384919",
    "19910263"
  ],
  "discriminant": "-6932288209941877830208203074656677634025259876817222666294567600128000000000",
  "regulator": "7269192462.723774923847794967989412479564020233867146390814",
  "points": [
    [
      "-8292917622739738520/1666681",
      "9625215452755632927037050910/2151685171"
    ],
    [
      "3368052387594167946820/2036329",
      "-195463910048947325366046123336070/2905841483"
    ],
    [
      "912300244109380/361",
      "-4039436560334810367110/6859"
    ],
    [
      "-4518623252060",
      "-6422667246649326290"
    ],
    [
      "1487314340902180/361",
      "30970288097683365740890/6859"
    ],
    [
      "1525745439369146800/654481",
      "536906454219172832722407410/529475129"
    ],
    [
      "942244363804542605380/117050761",
      "24970768788529311254657853116890/1266372183259"
    ],
    [
      "-1418409692545861820/436921",
      "-2456344447838241710847328490/288804781"
    ],
    [
      "-296569125732543830/117649",
      "-349841047483184978142132530/40353607"
    ],
    [
      "23214073942088966020/8048569",
      "-18178516331190421881673179370/22833790253"
    ]
  ],
  "submitter": "Maksym Voznyy",
  "history": [],
  "commentary": "t = 685/233 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 09:13:28",
  "updated_at": "2026-10-19 09:13:28"
}