{
  "id": 2337,
  "curve_key": "20736949043209:-71757692805680588773",
  "ainvs": [
    "1",
    "0",
    "1",
    "-432019771734",
    "83052849190112296"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 91.98881460885829,
  "faltings_height": 5.683389409141743,
  "conductor": "477446190",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "17",
    "23",
    "31",
    "101"
  ],
  "discriminant": "2180647130276544682241561486718657600",
  "regulator": "6.419821285169134474473999418060132482378",
  "points": [
    [
      "905549",
      "658641573"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-8, q=31; A=(3q-p)(p+q)^3=1228867, B=-(p+3q)(p-q)^3=5042115. 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 19:55:18",
  "updated_at": "2026-09-26 19:55:18"
}