{
  "id": 2495,
  "curve_key": "30774991681:4878091696546079",
  "ainvs": [
    "1",
    "0",
    "0",
    "-641145660",
    "-5645992892400"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 72.44990471610024,
  "faltings_height": 4.009504779696135,
  "conductor": "1005330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "23",
    "31",
    "47"
  ],
  "discriminant": "3096770542638476857344000000",
  "regulator": "5.579010668022010700390849658438017709105",
  "points": [
    [
      "-14820",
      "782580"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-23, q=8; A=(3q-p)(p+q)^3=-158625, B=-(p+3q)(p-q)^3=29791. 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 20:05:09",
  "updated_at": "2026-09-26 20:05:09"
}