{
  "id": 2297,
  "curve_key": "77512128394561:-673277527533909673441",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1614836008220",
    "779256263039024400"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 95.94436660637223,
  "faltings_height": 5.873418924809878,
  "conductor": "952220490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "31",
    "41",
    "113"
  ],
  "discriminant": "7176110317928259949220037267456000000",
  "regulator": "3.613159474133285805431677287745670265409",
  "points": [
    [
      "809320",
      "49002100"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-41, q=24; A=(3q-p)(p+q)^3=-555169, B=-(p+3q)(p-q)^3=8513375. 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 19:52:48",
  "updated_at": "2026-09-26 19:52:48"
}