{
  "id": 1073,
  "curve_key": "2372307841:-112794637527361",
  "ainvs": [
    "1",
    "0",
    "0",
    "-49423080",
    "130545230400"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    8,
    2
  ],
  "naive_height": 64.76138727257502,
  "faltings_height": 3.30095302862925,
  "conductor": "82110",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23"
  ],
  "discriminant": "363628103290905600000000",
  "regulator": "2.034865242181593696521637625278328301143",
  "points": [
    [
      "4760",
      "53720"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 82110bt2 = LMFDB 82110.bs5: https://www.lmfdb.org/EllipticCurve/Q/82110/bs/5\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 82110, minimal discriminant 363628103290905600000000, torsion ℤ/2ℤ × ℤ/8ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-23 15:25:04",
  "updated_at": "2026-09-23 15:25:04"
}