{
  "id": 2344,
  "curve_key": "17020871167041:-69641074921442392161",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-354601482647",
    "80603184624262319"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 91.3963842679992,
  "faltings_height": 5.473356293348497,
  "conductor": "21145410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "31",
    "53"
  ],
  "discriminant": "47012853349819651977318182976000000",
  "regulator": "6.080843701459796392805716970875460082577",
  "points": [
    [
      "375787",
      "20196886"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-33, q=20; A=(3q-p)(p+q)^3=-204321, B=-(p+3q)(p-q)^3=4019679. 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 19:55:43",
  "updated_at": "2026-09-26 19:55:43"
}