{
  "id": 2204,
  "curve_key": "3320300206381921:-116254232360128949147281",
  "ainvs": [
    "1",
    "0",
    "0",
    "-69172920966290",
    "134553503911665092100"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 107.21649479208038,
  "faltings_height": 6.975454128397751,
  "conductor": "43127978790",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "47",
    "73",
    "167",
    "193"
  ],
  "discriminant": "13361834109079990454820368569429852224000000",
  "regulator": "5.832860558377862359214034445383864412914",
  "points": [
    [
      "7375780",
      "5056689310"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=60; A=(3q-p)(p+q)^3=20037839, B=-(p+3q)(p-q)^3=64965839. 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 19:46:55",
  "updated_at": "2026-09-26 19:46:55"
}