{
  "id": 2340,
  "curve_key": "18901154228401:-73246986159185802601",
  "ainvs": [
    "1",
    "0",
    "0",
    "-393774046425",
    "84776571536405625"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 91.7107323192456,
  "faltings_height": 5.620547634469149,
  "conductor": "241766070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "59",
    "79"
  ],
  "discriminant": "802884837915008300662803339201000000",
  "regulator": "4.372489586394124645306382575011321396773",
  "points": [
    [
      "-519894",
      "386233227"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-49, q=10; A=(3q-p)(p+q)^3=-4686201, B=-(p+3q)(p-q)^3=-3902201. 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 19:55:29",
  "updated_at": "2026-09-26 19:55:29"
}