{
  "id": 2341,
  "curve_key": "123979721204761:-1380443260782624127741",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2582910858433",
    "1597735040292873056"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 97.35341738846519,
  "faltings_height": 5.755974244985566,
  "conductor": "273788130",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "29",
    "61",
    "67"
  ],
  "discriminant": "37694711863242919197029499552562500",
  "regulator": "4.801642409577602787961730668268817503139",
  "points": [
    [
      "-1849895",
      "213769502"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-58, q=3; A=(3q-p)(p+q)^3=-11147125, B=-(p+3q)(p-q)^3=-11122069. 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 19:55:32",
  "updated_at": "2026-09-26 19:55:32"
}