{
  "id": 2356,
  "curve_key": "15279086168641:-59530134929536222561",
  "ainvs": [
    "1",
    "0",
    "0",
    "-318314295180",
    "68900592605216400"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 91.07251827648383,
  "faltings_height": 5.40763971931953,
  "conductor": "458948490",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "29",
    "31"
  ],
  "discriminant": "13352399247779733424588329024000000",
  "regulator": "1.944050606420929501672319791739611237317",
  "points": [
    [
      "297360",
      "23092020"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-31, q=20; A=(3q-p)(p+q)^3=-121121, B=-(p+3q)(p-q)^3=3846879. 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 19:56:30",
  "updated_at": "2026-09-26 19:56:30"
}