{
  "id": 2802,
  "curve_key": "465:8775",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-10",
    "-8"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    2
  ],
  "naive_height": 18.426112216762068,
  "faltings_height": -0.4794896611649321,
  "conductor": "2725",
  "bad_primes": [
    "5",
    "109"
  ],
  "discriminant": "13625",
  "regulator": "1.80641455631543743874276132028102361313538",
  "points": [
    [
      "4",
      "0"
    ],
    [
      "19",
      "70"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 2725d1 = LMFDB 2725.a1: https://www.lmfdb.org/EllipticCurve/Q/2725/a/1\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 2725, minimal discriminant 13625, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:23:06",
  "updated_at": "2026-09-26 20:23:06"
}