{
  "id": 2311,
  "curve_key": "146464036200001:-1772234463500430300001",
  "ainvs": [
    "1",
    "0",
    "0",
    "-3051334087500",
    "2051197041440250000"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 97.8534030826784,
  "faltings_height": 5.8676236308133145,
  "conductor": "65934330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "23",
    "73"
  ],
  "discriminant": "630559943463009495824744841216000000",
  "regulator": "3.071875293987179679512850274990029797904",
  "points": [
    [
      "973080",
      "57820020"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-23, q=32; A=(3q-p)(p+q)^3=86751, B=-(p+3q)(p-q)^3=12145375. 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 19:53:41",
  "updated_at": "2026-09-26 19:53:41"
}