{
  "id": 1373,
  "curve_key": "188608:-81842176",
  "ainvs": [
    "0",
    "1",
    "0",
    "-3929",
    "93415"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    2
  ],
  "naive_height": 36.4422781982921,
  "faltings_height": 0.8037616519352179,
  "conductor": "4405696",
  "bad_primes": [
    "2",
    "23",
    "41",
    "73"
  ],
  "discriminant": "6485184512",
  "regulator": "12.66445480481246979325369448186401209380340478",
  "points": [
    [
      "-57",
      "368"
    ],
    [
      "-11",
      "368"
    ],
    [
      "127",
      "1288"
    ],
    [
      "219",
      "3128"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "This curve is due to Noam Elkies and is listed in his 2011 Oberwolfach report Moduli of Marked Elliptic Curves. Elkies gives the rank-4 curve with rational 2-torsion as \\((N;a_2,a_4)=(4405696;106,-184)\\), corresponding to \\(y^2=x^3+106x^2-184x\\). Its global minimal model has ainvs \\([0,1,0,-3929,93415]\\), rank 4, torsion \\(\\mathbf Z/2\\mathbf Z\\), and conductor \\(4405696\\).",
  "created_at": "2026-09-24 17:57:42",
  "updated_at": "2026-09-24 17:57:42"
}