{
  "id": 2810,
  "curve_key": "4249:-263357",
  "ainvs": [
    "1",
    "1",
    "0",
    "-88",
    "268"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "naive_height": 25.063316820344436,
  "faltings_height": 0.02724504995912796,
  "conductor": "141870",
  "bad_primes": [
    "2",
    "3",
    "5",
    "4729"
  ],
  "discriminant": "4256100",
  "regulator": "1.9526127387992785966930193950928491255628022",
  "points": [
    [
      "7",
      "4"
    ],
    [
      "6",
      "-2"
    ],
    [
      "9",
      "13"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 141870i1 = LMFDB 141870.a1: https://www.lmfdb.org/EllipticCurve/Q/141870/a/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 141870, minimal discriminant 4256100, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:23:25",
  "updated_at": "2026-09-26 20:23:25"
}