{
  "id": 3316,
  "curve_key": "180585:-83401461",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-3762",
    "97470"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    6
  ],
  "naive_height": 36.478352770322296,
  "faltings_height": 1.0013817805641303,
  "conductor": "342",
  "bad_primes": [
    "2",
    "3",
    "19"
  ],
  "discriminant": "-617336050482",
  "regulator": "2.129702711707007664362148315407992772030",
  "points": [
    [
      "39",
      "75"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 342c4 = LMFDB 342.c2: https://www.lmfdb.org/EllipticCurve/Q/342/c/2\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 342, minimal discriminant -617336050482, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:56:36",
  "updated_at": "2026-09-26 20:56:36"
}