{
  "id": 1565,
  "curve_key": "-13345290059912159:730570959120765242156111",
  "ainvs": [
    "1",
    "0",
    "0",
    "278026876248170",
    "-845568216554201565148"
  ],
  "rank_lower_bound": 3,
  "torsion": [
    8
  ],
  "naive_height": 111.3898197390175,
  "faltings_height": 7.366598207029397,
  "conductor": "1720479810",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "23",
    "29",
    "71",
    "173"
  ],
  "discriminant": "-1684309570465762737592659358826312666972160000",
  "regulator": "96.623867553846555292918691774531180317605139",
  "points": [
    [
      "1749252044",
      "73163266762778"
    ],
    [
      "3517309196/625",
      "468006709506794/15625"
    ],
    [
      "517436444",
      "11776060498778"
    ]
  ],
  "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 01:09:19",
  "updated_at": "2026-09-25 01:09:19"
}