{
  "id": 2512,
  "curve_key": "3253268929:-128949541916833",
  "ainvs": [
    "1",
    "0",
    "0",
    "-67776436",
    "149241506960"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 65.70877845628024,
  "faltings_height": 3.5049261379327583,
  "conductor": "1345890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "29"
  ],
  "discriminant": "10303141811083180396646400",
  "regulator": "1.851685272821862139489803122057492839938",
  "points": [
    [
      "-9016",
      "170156"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-17, q=4; A=(3q-p)(p+q)^3=-63713, B=-(p+3q)(p-q)^3=-46305. 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 20:06:12",
  "updated_at": "2026-09-26 20:06:12"
}