{
  "id": 2194,
  "curve_key": "6668197088929369:-544035578661914229554653",
  "ainvs": [
    "1",
    "0",
    "1",
    "-138920772686029",
    "629670797059743745556"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 109.30837775037102,
  "faltings_height": 6.878093911565811,
  "conductor": "2874451290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "17",
    "19",
    "29",
    "53",
    "193"
  ],
  "discriminant": "304217937162420208104061825062626075062500",
  "regulator": "8.448304962819542793106051473873946606858",
  "points": [
    [
      "-13603451",
      "1456419128"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=53; A=(3q-p)(p+q)^3=1323787, B=-(p+3q)(p-q)^3=82312875. 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 19:46:17",
  "updated_at": "2026-09-26 19:46:17"
}