{
  "id": 1409,
  "curve_key": "5684161676366236129:-13551930641167351143004481617",
  "ainvs": [
    "1",
    "0",
    "0",
    "-118420034924296586",
    "15685104898890172023674916"
  ],
  "rank_lower_bound": 2,
  "torsion": [
    12
  ],
  "naive_height": 129.55265306151645,
  "faltings_height": 8.396720119620005,
  "conductor": "5960311890",
  "bad_primes": [
    "2",
    "3",
    "5",
    "13",
    "157",
    "311",
    "313"
  ],
  "discriminant": "-752258682280058735862282494648154092281528320000",
  "regulator": "145.940315181359336411857676789208387287808",
  "points": [
    [
      "1014772465816564/5121169",
      "170975092752356183434/11589205447"
    ],
    [
      "1249863053030644/6285049",
      "135500105511564482546/15756617843"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/12. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-24 23:24:17",
  "updated_at": "2026-09-24 23:24:17"
}