{
  "id": 714,
  "curve_key": "1053116124816:-561027980838902040",
  "ainvs": [
    "0",
    "0",
    "1",
    "-21939919267",
    "649337940785766"
  ],
  "rank_lower_bound": 14,
  "torsion": [],
  "naive_height": 83.04832386893162,
  "faltings_height": 4.970090056474674,
  "conductor": "493755674212808044114451600614357",
  "bad_primes": [
    "4157",
    "455683",
    "260656913414353491310547"
  ],
  "discriminant": "493755674212808044114451600614357",
  "regulator": "144271421772647.139609736538521631190293467835698343613634502335904",
  "points": [
    [
      "-127138",
      "37197684"
    ],
    [
      "-1620",
      "26170142"
    ],
    [
      "-120",
      "25533717"
    ],
    [
      "1021005",
      "1021076132"
    ],
    [
      "-562064484938/3508129",
      "47271451162511756/6570725617"
    ],
    [
      "-189408467/1369",
      "1630693958927/50653"
    ],
    [
      "-477486407/4096",
      "10560152015789/262144"
    ],
    [
      "-20211714/169",
      "86848491956/2197"
    ],
    [
      "-1871/36",
      "5508966331/216"
    ],
    [
      "1358194/9",
      "751746968/27"
    ],
    [
      "7972092/49",
      "12771156999/343"
    ],
    [
      "102341593/729",
      "360822194945/19683"
    ],
    [
      "393676606/12769",
      "2150516645467/1442897"
    ],
    [
      "462062546/49",
      "9931108679528/343"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "From Michael Rubinstein's github repository:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-11 02:03:46",
  "updated_at": "2026-09-11 02:03:46"
}