{
  "id": 3213,
  "curve_key": "393:-7749",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-8",
    "11"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2
  ],
  "naive_height": 17.921428835607784,
  "faltings_height": -0.6676691866209351,
  "conductor": "377",
  "bad_primes": [
    "13",
    "29"
  ],
  "discriminant": "377",
  "regulator": "1.443894413560845861394701311935071148844",
  "points": [
    [
      "-2",
      "5"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 377a1 = LMFDB 377.a3: https://www.lmfdb.org/EllipticCurve/Q/377/a/3\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 377, minimal discriminant 377, torsion ℤ/2ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:42:58",
  "updated_at": "2026-09-26 20:42:58"
}