{
  "id": 2115,
  "curve_key": "4448541900271872776641:-258697230234220683802742368406689",
  "ainvs": [
    "1",
    "0",
    "0",
    "-92677956255664016180",
    "299418090541143369157794628752"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    10
  ],
  "naive_height": 149.54058999749896,
  "faltings_height": 10.447999882657193,
  "conductor": "108499668578070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "31",
    "71",
    "97",
    "11579"
  ],
  "discriminant": "12216593975275293347287354970642317946970972624418175452800000",
  "regulator": "535.13719622262266389425970186520886438086041",
  "points": [
    [
      "31916669443/4",
      "2085126412261619/8"
    ],
    [
      "-4390981096178312/426409",
      "112011007728122354595260/278445077"
    ],
    [
      "83895345337504/7921",
      "501454203572191862252/704969"
    ]
  ],
  "submitter": "Steps Unbounded",
  "history": [],
  "commentary": "Rank >= 3 with torsion Z/10 from the universal X_1(10) family at s=31/97 (t=s^2(2s-1)/(s-1)^2); conductor 108499668578070.",
  "created_at": "2026-09-26 08:51:42",
  "updated_at": "2026-09-26 08:51:42"
}