{
  "id": 2402,
  "curve_key": "4695598718721:-10163385132735524481",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-97824973307",
    "11763201693205739"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 87.53294022924821,
  "faltings_height": 5.072848301970157,
  "conductor": "5986890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "43"
  ],
  "discriminant": "137270129095476284680858176000000",
  "regulator": "4.944767893504102565909731418872061624855",
  "points": [
    [
      "153697",
      "18857976"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-39, q=4; A=(3q-p)(p+q)^3=-2186625, B=-(p+3q)(p-q)^3=-2146689. 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 19:59:22",
  "updated_at": "2026-09-26 19:59:22"
}