{
  "id": 2225,
  "curve_key": "1068018183743449:-16075088252532295288093",
  "ainvs": [
    "1",
    "0",
    "1",
    "-22250378827989",
    "18605424364010439436"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 103.81374348384229,
  "faltings_height": 6.705036742331219,
  "conductor": "927028830",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "43",
    "53",
    "149"
  ],
  "discriminant": "555463074754204515458033563316180599272900",
  "regulator": "4.605816423410060598638804184760271595919",
  "points": [
    [
      "4711223",
      "4281037788"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-10, q=53; A=(3q-p)(p+q)^3=13436683, B=-(p+3q)(p-q)^3=37257003. 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 19:48:14",
  "updated_at": "2026-09-26 19:48:14"
}