{
  "id": 3113,
  "curve_key": "5025:-212625",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-105",
    "272"
  ],
  "rank_lower_bound": 1,
  "torsion": [
    2,
    2
  ],
  "naive_height": 25.56654219878183,
  "faltings_height": 0.17247988596231864,
  "conductor": "275",
  "bad_primes": [
    "5",
    "11"
  ],
  "discriminant": "47265625",
  "regulator": "1.192245246213278814240774821427197468573",
  "points": [
    [
      "0",
      "16"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 275a2 = LMFDB 275.a3: https://www.lmfdb.org/EllipticCurve/Q/275/a/3\n\nMordell–Weil rank exactly 1 (Cremona's tables). Conductor 275, minimal discriminant 47265625, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.",
  "created_at": "2026-09-26 20:37:53",
  "updated_at": "2026-09-26 20:37:53"
}