{
  "id": 1055,
  "curve_key": "22651201:-107793784801",
  "ainvs": [
    "1",
    "0",
    "0",
    "-471900",
    "124722000"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    12
  ],
  "naive_height": 50.80717029831042,
  "faltings_height": 1.9293525111916436,
  "conductor": "4290",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13"
  ],
  "discriminant": "1335706803288000",
  "regulator": "2.145205242224710692465142794551165664586",
  "points": [
    [
      "402",
      "-48"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 4290bb4 = LMFDB 4290.bb5: https://www.lmfdb.org/EllipticCurve/Q/4290/bb/5\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 4290, minimal discriminant 1335706803288000, torsion ℤ/12ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-23 15:21:52",
  "updated_at": "2026-09-23 15:21:52"
}