{
  "id": 2301,
  "curve_key": "63780586402369:-503903027379115520353",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1328762216716",
    "583220985773421200"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 95.35940991483022,
  "faltings_height": 5.814872834631344,
  "conductor": "265887930",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "31",
    "47",
    "79"
  ],
  "discriminant": "3205334186424752223554818399803801600",
  "regulator": "3.477084356647905981629288612111595254060",
  "points": [
    [
      "563048",
      "116180276"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-55, q=8; A=(3q-p)(p+q)^3=-8202017, B=-(p+3q)(p-q)^3=-7751457. 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 19:53:04",
  "updated_at": "2026-09-26 19:53:04"
}