{
  "id": 2221,
  "curve_key": "1880484423305049:-81450199472866185580893",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-39176758818855",
    "94271073998895938025"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6,
    2
  ],
  "naive_height": 105.51091743159478,
  "faltings_height": 6.57206320005605,
  "conductor": "1076665590",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "17",
    "19",
    "37"
  ],
  "discriminant": "9071045513874506684513380942404552600900",
  "regulator": "6.335558136784002707542214431925877895449",
  "points": [
    [
      "-7221564",
      "763096509"
    ]
  ],
  "submitter": "Natanael Wildner Fraga",
  "history": [],
  "commentary": "Exact computational search in the full 2-torsion/3-torsion family with p=-54, q=37; A=(3q-p)(p+q)^3=-810645, B=-(p+3q)(p-q)^3=42953547. 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 19:47:59",
  "updated_at": "2026-09-26 19:47:59"
}