{
  "id": 1731,
  "curve_key": "-32469839:-10860041922409",
  "ainvs": [
    "1",
    "0",
    "0",
    "676455",
    "12569549337"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    10
  ],
  "naive_height": 60.03222258137109,
  "faltings_height": 3.060444537996617,
  "conductor": "140910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "61"
  ],
  "discriminant": "-68272420831874513100000",
  "regulator": "3.970073423704288975241127699224308196476",
  "points": [
    [
      "-336",
      "111093"
    ]
  ],
  "submitter": "hdeping",
  "history": [],
  "commentary": "Specialization u=-5/2 of the X_1(10) universal curve for torsion Z/10Z (Halbeisen-Hungerbuehler-Voznyy-Zargar 2021, Thm 4), y^2+xy=x^3+A(u)x^2+B(u)x.",
  "created_at": "2026-09-25 10:32:53",
  "updated_at": "2026-09-25 10:32:53"
}