{
  "id": 3234,
  "curve_key": "14689:-1780273",
  "ainvs": [
    "1",
    "0",
    "0",
    "-306",
    "2035"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2
  ],
  "naive_height": 28.784562579994244,
  "faltings_height": 0.00261613626544366,
  "conductor": "14705",
  "bad_primes": [
    "5",
    "17",
    "173"
  ],
  "discriminant": "14705",
  "regulator": "3.38731966177852374718933070726322964981873",
  "points": [
    [
      "9",
      "1"
    ],
    [
      "31/4",
      "65/8"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 14705a1 = LMFDB 14705.a1: https://www.lmfdb.org/EllipticCurve/Q/14705/a/1\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 14705, minimal discriminant 14705, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:43:56",
  "updated_at": "2026-09-26 20:43:56"
}