{
  "id": 2386,
  "curve_key": "5720671619721:-13588893326133090981",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-119180658744",
    "15727915589300208"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 88.12532199138802,
  "faltings_height": 5.192768245866566,
  "conductor": "3028410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "19",
    "23"
  ],
  "discriminant": "1479836157251574044321922080250000",
  "regulator": "4.828794103901928874622271539550714115328",
  "points": [
    [
      "-223413",
      "176755674"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-12, q=23; A=(3q-p)(p+q)^3=107811, B=-(p+3q)(p-q)^3=2443875. 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 19:58:20",
  "updated_at": "2026-09-26 19:58:20"
}