{
  "id": 2391,
  "curve_key": "9793340630089:-30638609815394556613",
  "ainvs": [
    "1",
    "0",
    "1",
    "-204027929794",
    "35461336950675476"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 89.73817122923894,
  "faltings_height": 5.208640149672696,
  "conductor": "56573790",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "17",
    "23",
    "53"
  ],
  "discriminant": "318399556614775800703661351174400",
  "regulator": "6.477932368128815046793569163062852437271",
  "points": [
    [
      "-111845/4",
      "1622837491/8"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-16, q=23; A=(3q-p)(p+q)^3=29155, B=-(p+3q)(p-q)^3=3143907. 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 19:58:38",
  "updated_at": "2026-09-26 19:58:38"
}