{
  "id": 812,
  "curve_key": "21050229245961:-104018701700013743205",
  "ainvs": [
    "1",
    "-1",
    "0",
    "-438546442624",
    "120392125493108044"
  ],
  "rank_lower_bound": 15,
  "torsion": [],
  "naive_height": 92.18220476181277,
  "faltings_height": 5.6379759624532415,
  "conductor": "431793384450914672704925243339122174",
  "bad_primes": [
    "2",
    "2797",
    "13469",
    "388477",
    "14752066382302142085667"
  ],
  "discriminant": "-863586768901829345409850486678244348",
  "regulator": "263818548239.76354305768355101205736891296057136096442359660547572376",
  "points": [
    [
      "337505",
      "-104214372"
    ],
    [
      "830308",
      "572896950"
    ],
    [
      "384631",
      "-93015561"
    ],
    [
      "756838",
      "-471550080"
    ],
    [
      "-349194",
      "480747530"
    ],
    [
      "633826",
      "-311861496"
    ],
    [
      "997802",
      "821832750"
    ],
    [
      "225627",
      "-181579850"
    ],
    [
      "458692",
      "-125697522"
    ],
    [
      "690406",
      "382676864"
    ],
    [
      "-528813",
      "-451866130"
    ],
    [
      "161302",
      "-232137750"
    ],
    [
      "-226338",
      "456245570"
    ],
    [
      "-743271",
      "189393268"
    ],
    [
      "1954172",
      "2592469090"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "From Michael Rubinstein's github repository:\r\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-21 00:39:24",
  "updated_at": "2026-09-21 00:39:24"
}