{
  "id": 2116,
  "curve_key": "12280572062268404610241:-1430806606429423110626793310848289",
  "ainvs": [
    "1",
    "0",
    "0",
    "-255845251297258429380",
    "1656026164827548903395128129552"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    10
  ],
  "naive_height": 152.68709282898638,
  "faltings_height": 10.661593988383892,
  "conductor": "72830908567230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "31",
    "107",
    "419",
    "9341"
  ],
  "discriminant": "-112930777037896130279891100939973298040636274393064790000000000",
  "regulator": "599.76761503045484535941432699537084745687451",
  "points": [
    [
      "-18555573606",
      "120528064225128"
    ],
    [
      "-63488808",
      "1293162519196140"
    ],
    [
      "14292069467975076/2036329",
      "1319184080857274967103524/2905841483"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Rank >= 3 with torsion Z/10 from the universal X_1(10) family at s=62/107 (t=s^2(2s-1)/(s-1)^2); conductor 72830908567230.",
  "created_at": "2026-09-26 08:51:45",
  "updated_at": "2026-09-26 08:51:45"
}