{
  "id": 2117,
  "curve_key": "-7159296095556645933119:-1382918387702921481611636139618721",
  "ainvs": [
    "1",
    "0",
    "0",
    "149152001990763456940",
    "1600599985779699566846031375600"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    10
  ],
  "naive_height": 152.61900821736822,
  "faltings_height": 10.794573472937167,
  "conductor": "108499668578070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "31",
    "71",
    "97",
    "11579"
  ],
  "discriminant": "-1319106895508418588215664322186016585562487022588867745937500000",
  "regulator": "4281.0975697809813111540776149216709150468833",
  "points": [
    [
      "-80935636336739255/1405950016",
      "66516321367557727744706803415/52717501799936"
    ],
    [
      "-287110248805781/77284",
      "21433670546066245100009/21484952"
    ],
    [
      "169280993000247820/49434961",
      "509825053368117738000824240/347577210791"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Rank >= 3 with torsion Z/10 from the universal X_1(10) family at s=97/132 (t=s^2(2s-1)/(s-1)^2); conductor 108499668578070.",
  "created_at": "2026-09-26 08:51:49",
  "updated_at": "2026-09-26 08:51:49"
}