{
  "id": 2813,
  "curve_key": "129961:-53346709",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2708",
    "61518"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    3
  ],
  "naive_height": 35.58464569367299,
  "faltings_height": 0.9475582095917828,
  "conductor": "356590",
  "bad_primes": [
    "2",
    "5",
    "13",
    "211"
  ],
  "discriminant": "-376648187500",
  "regulator": "3.0947096830247695209214061492047590846080619",
  "points": [
    [
      "39",
      "105"
    ],
    [
      "27",
      "77"
    ],
    [
      "-61",
      "5"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 356590d1 = LMFDB 356590.d1: https://www.lmfdb.org/EllipticCurve/Q/356590/d/1\n\nMordell–Weil rank exactly 3 (Cremona's tables). Conductor 356590, minimal discriminant -376648187500, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:23:35",
  "updated_at": "2026-09-26 20:23:35"
}