{
  "id": 2119,
  "curve_key": "16024744135856503516561:-19974378567572561802662829425028025",
  "ainvs": [
    "1",
    "0",
    "0",
    "-333848836163677156595",
    "23118493712440422090809079478881"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    10
  ],
  "naive_height": 157.9595168989248,
  "faltings_height": 11.221086992689111,
  "conductor": "96439541661606",
  "bad_primes": [
    "2",
    "3",
    "11",
    "13",
    "31",
    "41",
    "43",
    "271",
    "7589"
  ],
  "discriminant": "-228507387882028771723106382409730412061916697717699303743385320448",
  "regulator": "2178.8695649252913568090534905874641142633198",
  "points": [
    [
      "7314361646176/289",
      "27301816244143729535/4913"
    ],
    [
      "28478480584450/2209",
      "475291182957696385007/103823"
    ],
    [
      "13693435267862145094/641659561",
      "82419936980414853145273031435/16253878339691"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Rank >= 3 with torsion Z/10 from the universal X_1(10) family at s=82/121 (t=s^2(2s-1)/(s-1)^2); conductor 96439541661606.",
  "created_at": "2026-09-26 08:51:56",
  "updated_at": "2026-09-26 08:51:56"
}