{
  "id": 1615,
  "curve_key": "81959368904687117843182484161:14874810415540931437165014518510121099080159",
  "ainvs": [
    "1",
    "0",
    "0",
    "-1707486852180981621732968420",
    "-17216215758728072194697189293040377167600"
  ],
  "rank_lower_bound": 4,
  "torsion": [
    6,
    2
  ],
  "naive_height": 199.7280634024196,
  "faltings_height": 14.681642557994104,
  "conductor": "10653519586931119470",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "23",
    "31",
    "199",
    "409",
    "4729",
    "9049"
  ],
  "discriminant": "190560654339073620935572242783982607067139442478388938178243220139854021001216000000",
  "regulator": "9553.539061890237756573804545075037780075153003",
  "points": [
    [
      "-17130074877560",
      "83704977705322388380"
    ],
    [
      "45737732696440",
      "19178307137128268380"
    ],
    [
      "59532139111240",
      "303512474592782012380"
    ],
    [
      "7050269797405926358600/129800449",
      "331618023454276743311087512030940/1478816515457"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/6+Z/2. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-25 01:38:07",
  "updated_at": "2026-09-25 01:38:07"
}