{
  "id": 2214,
  "curve_key": "4135604982464761:-265874263495494306217741",
  "ainvs": [
    "1",
    "0",
    "1",
    "-86158437134683",
    "307724834828804204306"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 107.8752300612441,
  "faltings_height": 6.7213665213214915,
  "conductor": "6060428430",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "83",
    "113",
    "181"
  ],
  "discriminant": "24926681213789409854798694891246162562500",
  "regulator": "6.109352244790208259350345762478860590032",
  "points": [
    [
      "5436790",
      "59559617"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=49; A=(3q-p)(p+q)^3=610875, B=-(p+3q)(p-q)^3=64611931. 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 19:47:33",
  "updated_at": "2026-09-26 19:47:33"
}