{
  "id": 1021,
  "curve_key": "20593:-2954665",
  "ainvs": [
    "1",
    "0",
    "0",
    "-429",
    "3384"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    4,
    2
  ],
  "naive_height": 29.798119473616044,
  "faltings_height": 0.19452204862694217,
  "conductor": "429",
  "bad_primes": [
    "3",
    "11",
    "13"
  ],
  "discriminant": "1656369",
  "regulator": "2.115453196439503695102406459953893088052",
  "points": [
    [
      "24",
      "72"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 429b2 = LMFDB 429.b4: https://www.lmfdb.org/EllipticCurve/Q/429/b/4\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 429, minimal discriminant 1656369, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-23 15:16:30",
  "updated_at": "2026-09-23 15:16:30"
}