{
  "id": 2237,
  "curve_key": "1988750105301969:-88669337432520176265753",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-41432293860458",
    "102626558312379224681"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 105.6788482455881,
  "faltings_height": 6.5279629264333545,
  "conductor": "2589817230",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "89"
  ],
  "discriminant": "2029976792628159061494504666720997646400",
  "regulator": "3.875392621704418816037795023423542011066",
  "points": [
    [
      "3794967",
      "214016071"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-51, q=38; A=(3q-p)(p+q)^3=-362505, B=-(p+3q)(p-q)^3=44413047. 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 19:48:58",
  "updated_at": "2026-09-26 19:48:58"
}