{
  "id": 2940,
  "curve_key": "4465:207575",
  "ainvs": [
    "1",
    "0",
    "0",
    "-93",
    "-248"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    2
  ],
  "naive_height": 25.2120734799318,
  "faltings_height": 0.13007573983013063,
  "conductor": "279775",
  "bad_primes": [
    "5",
    "19",
    "31"
  ],
  "discriminant": "26578625",
  "regulator": "4.9813548651026408876619040602206395640292662",
  "points": [
    [
      "11",
      "4"
    ],
    [
      "12",
      "14"
    ],
    [
      "-4",
      "10"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 279775c1 = LMFDB 279775.c2: https://www.lmfdb.org/EllipticCurve/Q/279775/c/2\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 279775, minimal discriminant 26578625, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:29:18",
  "updated_at": "2026-09-26 20:29:18"
}