{
  "id": 3494,
  "curve_key": "125397090703365721:-89596230560443380675349981",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2612439389653453",
    "103699340708735815532756"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    6
  ],
  "naive_height": 119.51471096263025,
  "faltings_height": 8.00513918835631,
  "conductor": "23340040158996330",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "11",
    "17",
    "37",
    "227",
    "1201",
    "58921"
  ],
  "discriminant": "-3504448328079385480608964470344818871253999937500",
  "regulator": "5497.1822864696564248373510912814768720271278889714",
  "points": [
    [
      "212804215/4",
      "2716167473161/8"
    ],
    [
      "202535671",
      "2807520819644"
    ],
    [
      "359311405",
      "6749176323872"
    ],
    [
      "851679685/16",
      "21745371395333/64"
    ],
    [
      "5921980345/256",
      "966168902510597/4096"
    ],
    [
      "11103921025/49",
      "1145226165790286/343"
    ]
  ],
  "submitter": "jesper-petersen",
  "history": [],
  "commentary": "Torsion Z/6 specialization of the universal Tate family\r\ny^2 + t*x*y + (t+2)*y = x^3\r\nat t = -8431/8415. Found in a conductor-oriented search of reduced\r\nrational parameters, using bad-reduction support filtering followed by\r\nMestre-Nagao screening and exact PARI/GP descent. PARI/GP 2.17.4 gives\r\nrank bounds [6,6] and torsion Z/6Z.",
  "created_at": "2026-09-27 10:57:18",
  "updated_at": "2026-09-27 10:57:18"
}