{
  "id": 2758,
  "curve_key": "633:2835",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-13",
    "0"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 19.351411266432528,
  "faltings_height": -0.3210955963409625,
  "conductor": "377",
  "bad_primes": [
    "13",
    "29"
  ],
  "discriminant": "142129",
  "regulator": "2.887788827121691722789402623870142297688",
  "points": [
    [
      "-9/4",
      "39/8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 377a2 = LMFDB 377.a2: https://www.lmfdb.org/EllipticCurve/Q/377/a/2\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 377, minimal discriminant 142129, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:21:07",
  "updated_at": "2026-09-26 20:21:07"
}