{
  "id": 1663,
  "curve_key": "5840149517260321:-450669902829365861640881",
  "ainvs": [
    "1",
    "1",
    "1",
    "-121669781609590",
    "521608633134542224755"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    5
  ],
  "naive_height": 108.93004420323673,
  "faltings_height": 6.941100191313834,
  "conductor": "53288164177430",
  "bad_primes": [
    "2",
    "5",
    "7",
    "13",
    "17",
    "29",
    "6359",
    "18679"
  ],
  "discriminant": "-2263517822302726032995989524077399244800000",
  "regulator": "552.782958215057760093635665497217534440339204776",
  "points": [
    [
      "54147817/9",
      "73219351061/27"
    ],
    [
      "158630377/9",
      "1675656259861/27"
    ],
    [
      "41078761/9",
      "211433330965/27"
    ],
    [
      "8013773",
      "7820548943"
    ],
    [
      "272153313",
      "4485965145743"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Torsion Z/5. From Michael Rubinstein's github repository:\nhttps://github.com/mrubinst/elliptic-curves-by-rank",
  "created_at": "2026-09-25 02:40:19",
  "updated_at": "2026-09-25 02:40:19"
}