{
  "id": 2503,
  "curve_key": "10870244641:-1125814482016561",
  "ainvs": [
    "1",
    "0",
    "0",
    "-226463430",
    "1303007148900"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 69.32788513169409,
  "faltings_height": 3.6249672135044557,
  "conductor": "1111110",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "37"
  ],
  "discriminant": "9834476331017834496000000",
  "regulator": "1.546996200522784560357742642493990056285",
  "points": [
    [
      "-14790",
      "1197870"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=8; A=(3q-p)(p+q)^3=-4625, B=-(p+3q)(p-q)^3=101871. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.",
  "created_at": "2026-09-26 20:05:39",
  "updated_at": "2026-09-26 20:05:39"
}