{
  "id": 3217,
  "curve_key": "513:351",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-11",
    "2"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2
  ],
  "naive_height": 18.72082753551231,
  "faltings_height": -0.37174608346801735,
  "conductor": "3717",
  "bad_primes": [
    "3",
    "7",
    "59"
  ],
  "discriminant": "78057",
  "regulator": "0.925178410832445646886214715253508702948947",
  "points": [
    [
      "0",
      "1"
    ],
    [
      "-2",
      "4"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 3717b1 = LMFDB 3717.a2: https://www.lmfdb.org/EllipticCurve/Q/3717/a/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 3717, minimal discriminant 78057, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:43:08",
  "updated_at": "2026-09-26 20:43:08"
}