{
  "id": 2312,
  "curve_key": "41214295441881:-236224234732322056221",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-858631155039",
    "273407893746124473"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 94.04941886653862,
  "faltings_height": 5.814772787645739,
  "conductor": "112342230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29",
    "43"
  ],
  "discriminant": "8220752981194140677239024315302562500",
  "regulator": "3.648235968938818284788972966801925519655",
  "points": [
    [
      "-4194537/4",
      "1154733927/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-54, q=11; A=(3q-p)(p+q)^3=-6917109, B=-(p+3q)(p-q)^3=-5767125. 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 19:53:45",
  "updated_at": "2026-09-26 19:53:45"
}