{
  "id": 1490,
  "curve_key": "442361850153765547680574124481:-2706725559984831806787018330823363830548820129",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-9215871878203448910011960927",
    "3132784212945409487749240767092972677236551"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    12
  ],
  "naive_height": 209.2241376172318,
  "faltings_height": 15.493113551658414,
  "conductor": "100083125799386730",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29",
    "41",
    "43",
    "47",
    "277",
    "1669"
  ],
  "discriminant": "-4189699142318856327882262802577046051340516971886176240499434511726099186199822336000000",
  "regulator": "4764.3152023851567631746884545571725838058885",
  "points": [
    [
      "8103305093885315790099",
      "729446233182561054772360338776374"
    ],
    [
      "-547353845340903001245/3352561",
      "3280259079595753651406085084442/6138539191"
    ],
    [
      "-8461133439977752610040329781/51970300975849",
      "211209288746037114333678415677737308596178/374656134457837402507"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/12. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-25 00:34:19",
  "updated_at": "2026-09-25 00:34:19"
}