{
  "id": 4096,
  "curve_key": "109687808120464:-275303529765002578112",
  "ainvs": [
    "0",
    "-1",
    "0",
    "-2285162669176",
    "318639106356309376"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    2
  ],
  "naive_height": 96.98597801598073,
  "faltings_height": 6.146820577831318,
  "conductor": "825030649904725540797360",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "17",
    "23",
    "59",
    "61",
    "269",
    "8689",
    "21329569"
  ],
  "discriminant": "719853896926134270305087550901440537600",
  "regulator": "2184041.006599097595305587856530816245100724798251947458721",
  "points": [
    [
      "-303732",
      "-992318404"
    ],
    [
      "-1514884",
      "551294820"
    ],
    [
      "1652236",
      "1026362820"
    ],
    [
      "23375800",
      "-112783388976"
    ],
    [
      "-625704",
      "1226176000"
    ],
    [
      "-828242",
      "-1281852054"
    ],
    [
      "409342/9",
      "12513514258/27"
    ],
    [
      "-237239",
      "-920552220"
    ],
    [
      "6616024",
      "16576942080"
    ],
    [
      "1470838",
      "373485546"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/2. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-09 14:50:51",
  "updated_at": "2026-10-09 14:50:51"
}