{
  "id": 2641,
  "curve_key": "2766339589561:-4358135895974240941",
  "ainvs": [
    "1",
    "0",
    "1",
    "-57632074783",
    "5044133965815806"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 85.94563834330133,
  "faltings_height": 5.104270748387053,
  "conductor": "124061070",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "19",
    "31",
    "59"
  ],
  "discriminant": "1259512682759418221306581370062500",
  "regulator": "10.9805377637367959501846906225339610080605",
  "points": [
    [
      "-240203",
      "71031578"
    ],
    [
      "-65735",
      "92491142"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-38, q=7; A=(3q-p)(p+q)^3=-1757669, B=-(p+3q)(p-q)^3=-1549125. 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 20:14:45",
  "updated_at": "2026-09-26 20:14:45"
}