{
  "id": 2665,
  "curve_key": "565648599961:-420408098098164541",
  "ainvs": [
    "1",
    "0",
    "1",
    "-11784345833",
    "486582464844056"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6,
    2
  ],
  "naive_height": 81.18371662265444,
  "faltings_height": 4.637676264154007,
  "conductor": "31141110",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "61"
  ],
  "discriminant": "2454292447815656063338785562500",
  "regulator": "4.34460678347978652192451705344753661387223",
  "points": [
    [
      "-124548",
      "4783399"
    ],
    [
      "-102435",
      "24928342"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-22, q=13; A=(3q-p)(p+q)^3=-44469, B=-(p+3q)(p-q)^3=728875. 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 20:16:38",
  "updated_at": "2026-09-26 20:16:38"
}