{
  "id": 2838,
  "curve_key": "3179521:-4895313569",
  "ainvs": [
    "1",
    "1",
    "1",
    "-66240",
    "5638272"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    4,
    2
  ],
  "naive_height": 44.91672334343959,
  "faltings_height": 1.7325590791668377,
  "conductor": "21945",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "19"
  ],
  "discriminant": "4733106325880625",
  "regulator": "2.75124709237994393042223779745915640788859",
  "points": [
    [
      "92",
      "531"
    ],
    [
      "22",
      "2036"
    ]
  ],
  "submitter": "David Renshaw",
  "history": [],
  "commentary": "Cremona 21945l2 = LMFDB 21945.l4: https://www.lmfdb.org/EllipticCurve/Q/21945/l/4\n\nMordell–Weil rank exactly 2 (Cremona's tables). Conductor 21945, minimal discriminant 4733106325880625, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.",
  "created_at": "2026-09-26 20:24:43",
  "updated_at": "2026-09-26 20:24:43"
}