{
  "id": 2647,
  "curve_key": "1529135077969:-1830020529456712153",
  "ainvs": [
    "1",
    "0",
    "0",
    "-31856980791",
    "2118076661752425"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 84.16717014890638,
  "faltings_height": 4.932244145146984,
  "conductor": "224970690",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "29",
    "41",
    "53"
  ],
  "discriminant": "131094448441250617176575832129600",
  "regulator": "37.8113412339573433901087400747980526977544",
  "points": [
    [
      "-158862",
      "56379741"
    ],
    [
      "-337009/4",
      "519045625/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-35, q=6; A=(3q-p)(p+q)^3=-1292617, B=-(p+3q)(p-q)^3=-1171657. 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 20:15:16",
  "updated_at": "2026-09-26 20:15:16"
}