{
  "id": 2427,
  "curve_key": "1766027219049:-2344396151488723893",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-36792233730",
    "2713430669688900"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 84.5992608924497,
  "faltings_height": 4.825854981444791,
  "conductor": "8534610",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "19",
    "23",
    "31"
  ],
  "discriminant": "6819706902311369803777138736400",
  "regulator": "9.050238410080564194513018707851204140743",
  "points": [
    [
      "-638745/4",
      "538288395/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-12, q=19; A=(3q-p)(p+q)^3=23667, B=-(p+3q)(p-q)^3=1340595. 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 20:00:55",
  "updated_at": "2026-09-26 20:00:55"
}