{
  "id": 2307,
  "curve_key": "53096338872241:-311653719347657385961",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1106173726505",
    "360710231137904025"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 94.80938728202209,
  "faltings_height": 5.908019642942044,
  "conductor": "765899310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19",
    "23",
    "47",
    "113"
  ],
  "discriminant": "30417988133469447014391389390625000000",
  "regulator": "5.319281750082326981268365886804805362664",
  "points": [
    [
      "-1171340",
      "222607795"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=22; A=(3q-p)(p+q)^3=-1765625, B=-(p+3q)(p-q)^3=6241671. 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 19:53:26",
  "updated_at": "2026-09-26 19:53:26"
}