{
  "id": 3250,
  "curve_key": "640:-16768",
  "ainvs": [
    "0",
    "1",
    "0",
    "-13",
    "15"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    3
  ],
  "naive_height": 19.454455174241538,
  "faltings_height": -0.4578030138692401,
  "conductor": "172",
  "bad_primes": [
    "2",
    "43"
  ],
  "discriminant": "-11008",
  "regulator": "0.7601396630066703586209147466874986291317",
  "points": [
    [
      "2",
      "1"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 172a1 = LMFDB 172.a1: https://www.lmfdb.org/EllipticCurve/Q/172/a/1\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 172, minimal discriminant -11008, torsion ℤ/3ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:45:54",
  "updated_at": "2026-09-26 20:45:54"
}