{
  "id": 3116,
  "curve_key": "78897:21887415",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-1644",
    "-24922"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 33.827695449892175,
  "faltings_height": 0.6933969608067919,
  "conductor": "289",
  "bad_primes": [
    "17"
  ],
  "discriminant": "6975757441",
  "regulator": "6.070512355460664321664107206543494672104",
  "points": [
    [
      "-589/25",
      "3594/125"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 289a2 = LMFDB 289.a2: https://www.lmfdb.org/EllipticCurve/Q/289/a/2\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 289, minimal discriminant 6975757441, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:38:02",
  "updated_at": "2026-09-26 20:38:02"
}