{
  "id": 4051,
  "curve_key": "784104579216:-563045048209964736",
  "ainvs": [
    "0",
    "0",
    "0",
    "-16335512067",
    "651672509502274"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    2,
    2
  ],
  "naive_height": 82.16342472077417,
  "faltings_height": 4.852783117888516,
  "conductor": "10859531085360",
  "bad_primes": [
    "2",
    "3",
    "5",
    "47",
    "61",
    "83",
    "241",
    "263"
  ],
  "discriminant": "95522826469059113081126976000000",
  "regulator": "962.89742178132225561524146375635320203987929171869",
  "points": [
    [
      "-13417",
      "29469150"
    ],
    [
      "379505",
      "221608008"
    ],
    [
      "492057/4",
      "179543525/8"
    ],
    [
      "-139657",
      "14462370"
    ],
    [
      "26033",
      "-15622200"
    ],
    [
      "-131767",
      "22723200"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/2+Z/2. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-10-07 22:24:44",
  "updated_at": "2026-10-07 22:24:44"
}