{
  "id": 3006,
  "curve_key": "-229904:-119573144",
  "ainvs": [
    "0",
    "-1",
    "1",
    "4790",
    "136798"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    5
  ],
  "naive_height": 37.19887765154207,
  "faltings_height": 1.2159598428395157,
  "conductor": "87515",
  "bad_primes": [
    "5",
    "23",
    "761"
  ],
  "discriminant": "-15306428196875",
  "regulator": "9.47197071070601930064228082236823597463274",
  "points": [
    [
      "64",
      "837"
    ],
    [
      "139",
      "1862"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 87515b1 = LMFDB 87515.a2: https://www.lmfdb.org/EllipticCurve/Q/87515/a/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 87515, minimal discriminant -15306428196875, torsion ℤ/5ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:33:01",
  "updated_at": "2026-09-26 20:33:01"
}