{
  "id": 685,
  "curve_key": "840544018041:-643804067688683085",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-17511333709",
    "745147974695329"
  ],
  "rank_lower_bound": 14,
  "torsion": [],
  "naive_height": 82.37194547904045,
  "faltings_height": 4.863211445129059,
  "conductor": "51901807229711945130373780604666",
  "bad_primes": [
    "2",
    "26640112403",
    "974128908402563115311"
  ],
  "discriminant": "103803614459423890260747561209332",
  "regulator": "1965047475033.57742796431515409297424241395231633244235334564296383",
  "points": [
    [
      "-85915",
      "40235703"
    ],
    [
      "-1619",
      "27812580"
    ],
    [
      "564",
      "27115613"
    ],
    [
      "708",
      "27069007"
    ],
    [
      "2064",
      "26626273"
    ],
    [
      "33852",
      "13808645"
    ],
    [
      "102032",
      "4491105"
    ],
    [
      "116870",
      "17113297"
    ],
    [
      "124358",
      "22088385"
    ],
    [
      "183630",
      "60912413"
    ],
    [
      "26171988",
      "133877339005"
    ],
    [
      "-8046479/64",
      "15891006891/512"
    ],
    [
      "1383280/9",
      "1106070619/27"
    ],
    [
      "6295744/9",
      "15519675125/27"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "From Michael Rubinstein's github repository:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-09 03:39:26",
  "updated_at": "2026-09-09 03:39:26"
}