{
  "id": 3325,
  "curve_key": "103999801:-1060593014701",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2166663",
    "1227357656"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    6
  ],
  "naive_height": 55.37969863092683,
  "faltings_height": 1.9650725699267206,
  "conductor": "25870",
  "bad_primes": [
    "2",
    "5",
    "13",
    "199"
  ],
  "discriminant": "16087906250",
  "regulator": "19.6282103989080732238258226901805611295247",
  "points": [
    [
      "1450",
      "32962"
    ],
    [
      "-1588",
      "26564"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 25870b2 = LMFDB 25870.a2: https://www.lmfdb.org/EllipticCurve/Q/25870/a/2\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 25870, minimal discriminant 16087906250, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:58:04",
  "updated_at": "2026-09-26 20:58:04"
}