{
  "id": 2378,
  "curve_key": "4947630395841:-3214613956475699361",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-103075633247",
    "3720643774088519"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 87.68978960994308,
  "faltings_height": 5.370323968370267,
  "conductor": "8584290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "23",
    "29"
  ],
  "discriminant": "64108525348908014315503878144000000",
  "regulator": "2.641114765180300995148689829997051211328",
  "points": [
    [
      "-331481",
      "38443122"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-39, q=16; A=(3q-p)(p+q)^3=-1058529, B=-(p+3q)(p-q)^3=1497375. 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 19:57:51",
  "updated_at": "2026-09-26 19:57:51"
}