{
  "id": 1567,
  "curve_key": "8719928024641:-32024451698994254689",
  "ainvs": [
    "1",
    "0",
    "0",
    "-181665167180",
    "37065322475812752"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    8
  ],
  "naive_height": 89.82606280099687,
  "faltings_height": 5.4907171448216125,
  "conductor": "2615851410",
  "bad_primes": [
    "2",
    "3",
    "5",
    "19",
    "23",
    "61",
    "3271"
  ],
  "discriminant": "-209795762244854805061067328094560000",
  "regulator": "121.32225006217315230008862965360590940337079",
  "points": [
    [
      "687334",
      "486397168"
    ],
    [
      "86264056/289",
      "476475370244/4913"
    ],
    [
      "8642116/25",
      "15578411096/125"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/8. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-25 01:11:19",
  "updated_at": "2026-09-25 01:11:19"
}