{
  "id": 1058,
  "curve_key": "21837841:-102047808889",
  "ainvs": [
    "1",
    "0",
    "0",
    "-454955",
    "118072977"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    10
  ],
  "naive_height": 50.69746454592934,
  "faltings_height": 1.8788362897524418,
  "conductor": "6270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "19"
  ],
  "discriminant": "301547812500000",
  "regulator": "2.707225460165105267594076124603183086339",
  "points": [
    [
      "418",
      "781"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 6270r2 = LMFDB 6270.r2: https://www.lmfdb.org/EllipticCurve/Q/6270/r/2\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 6270, minimal discriminant 301547812500000, torsion ℤ/10ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-23 15:22:54",
  "updated_at": "2026-09-23 15:22:54"
}