{
  "id": 2491,
  "curve_key": "38525329921:-7542568017089281",
  "ainvs": [
    "1",
    "0",
    "0",
    "-802611040",
    "8729757209600"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 73.12374534579487,
  "faltings_height": 3.9021557359369363,
  "conductor": "4975530",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "29",
    "43"
  ],
  "discriminant": "167246907063730675776000000",
  "regulator": "4.132610143741552234679024245129346546478",
  "points": [
    [
      "-11410",
      "4055660"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-7, q=12; A=(3q-p)(p+q)^3=5375, B=-(p+3q)(p-q)^3=198911. 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 20:04:54",
  "updated_at": "2026-09-26 20:04:54"
}