{
  "id": 2408,
  "curve_key": "2475391518601:-3148573143255012901",
  "ainvs": [
    "1",
    "0",
    "1",
    "-51570656638",
    "3644177581212656"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 85.61225906631698,
  "faltings_height": 5.140837872096749,
  "conductor": "23993970",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "47"
  ],
  "discriminant": "3040859411561698709871352464000000",
  "regulator": "8.643922919358779135052881607287070738256",
  "points": [
    [
      "-1013285/4",
      "171113071/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-32, q=15; A=(3q-p)(p+q)^3=-378301, B=-(p+3q)(p-q)^3=1349699. 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 19:59:46",
  "updated_at": "2026-09-26 19:59:46"
}