{
  "id": 1491,
  "curve_key": "169510784577932419577070562824001:-2201746305863415188473063174248164783412460236001",
  "ainvs": [
    "1",
    "0",
    "0",
    "-3531474678706925407855636725500",
    "2548317483638211729406118411284184511350250000"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    12
  ],
  "naive_height": 222.63140802133904,
  "faltings_height": 16.358506552233894,
  "conductor": "13906060693760505270",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "13",
    "29",
    "47",
    "53",
    "127",
    "139",
    "173",
    "2099"
  ],
  "discriminant": "13321857419362678573964021530884473816081419741034275700706566021324971123408896000000000000",
  "regulator": "620.88972271170820987011785884838975056750020",
  "points": [
    [
      "1128191793464920",
      "343676008705077502180"
    ],
    [
      "2507878946092152778360/2217121",
      "3291821431707000731684655232900/3301293169"
    ],
    [
      "6373869589832779000/529",
      "15906742017650602471721841500/12167"
    ]
  ],
  "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 00:35:19",
  "updated_at": "2026-09-25 00:35:19"
}