{
  "id": 2693,
  "curve_key": "17953:2168495",
  "ainvs": [
    "1",
    "0",
    "0",
    "-374",
    "-2541"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4,
    2
  ],
  "naive_height": 29.386537532612486,
  "faltings_height": 0.4219604214216633,
  "conductor": "759",
  "bad_primes": [
    "3",
    "11",
    "23"
  ],
  "discriminant": "627352209",
  "regulator": "2.983073350512852707175595929097206163060",
  "points": [
    [
      "34",
      "139"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 759b2 = LMFDB 759.b5: https://www.lmfdb.org/EllipticCurve/Q/759/b/5\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 759, minimal discriminant 627352209, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:18:03",
  "updated_at": "2026-09-26 20:18:03"
}