{
  "id": 2256,
  "curve_key": "476154587996521:5340301861913329391819",
  "ainvs": [
    "1",
    "0",
    "1",
    "-9919887249928",
    "-6180905759427327994"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 101.3902910464017,
  "faltings_height": 6.499017228132409,
  "conductor": "6168032310",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "17",
    "47",
    "149",
    "157"
  ],
  "discriminant": "45970175892705561815994668993334320250000",
  "regulator": "4.790674225363560905385161499664470385670",
  "points": [
    [
      "3520465",
      "1588200887"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-4, q=51; A=(3q-p)(p+q)^3=16300211, B=-(p+3q)(p-q)^3=24789875. 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 19:50:09",
  "updated_at": "2026-09-26 19:50:09"
}