{
  "id": 2120,
  "curve_key": "54691536397741200727201:-3708348268482159590840853980530801",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1139407008286275015150",
    "4292069755092734127597502522500"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    10
  ],
  "naive_height": 157.06798776805476,
  "faltings_height": 11.151923584643097,
  "conductor": "496968673605690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "23",
    "109",
    "131",
    "20749"
  ],
  "discriminant": "86712683041027272836190792582217933128613628580276332010000000000",
  "regulator": "1060.6270835322219053398758218169800666311430",
  "points": [
    [
      "2780042921700",
      "4634951021303474850"
    ],
    [
      "-3482260326681300/388129",
      "898021479468687051769950/241804367"
    ],
    [
      "2216018023802470188/583850569",
      "2097357498381358527975729462/14107581298747"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Rank >= 3 with torsion Z/10 from the universal X_1(10) family at s=46/131 (t=s^2(2s-1)/(s-1)^2); conductor 496968673605690.",
  "created_at": "2026-09-26 08:51:58",
  "updated_at": "2026-09-26 08:51:58"
}