{
  "id": 2373,
  "curve_key": "48092317390681:-333509726898900867421",
  "ainvs": [
    "1",
    "0",
    "1",
    "-1001923278973",
    "386006544861602756"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 94.51243067602783,
  "faltings_height": 5.508499211217359,
  "conductor": "14037870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "59",
    "103"
  ],
  "discriminant": "1497624463101900444408489762562500",
  "regulator": "7.468153501655425656640825942675506119593",
  "points": [
    [
      "-1137665",
      "231655352"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-22, q=27; A=(3q-p)(p+q)^3=12875, B=-(p+3q)(p-q)^3=6941291. 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 19:57:32",
  "updated_at": "2026-09-26 19:57:32"
}