{
  "id": 3490,
  "curve_key": "114083798090569:-446579947324466259013",
  "ainvs": [
    "1",
    "0",
    "1",
    "-2376745793554",
    "516874740970797596"
  ],
  "rank_lower_bound": 5,
  "torsion": [
    6
  ],
  "naive_height": 97.1038630957818,
  "faltings_height": 6.151516048953069,
  "conductor": "591998388510",
  "bad_primes": [
    "2",
    "3",
    "5",
    "23",
    "31",
    "103",
    "167",
    "1609"
  ],
  "discriminant": "743854093030240479885720191052127274280",
  "regulator": "48261.1883179379852781996820613634028508079492542",
  "points": [
    [
      "5894749735/4",
      "452576670634201/8"
    ],
    [
      "-710290010/841",
      "33820301854453/24389"
    ],
    [
      "206837986/1849",
      "39939448348439/79507"
    ],
    [
      "5107229935/484",
      "361096172573651/10648"
    ],
    [
      "81402874726/50625",
      "10508466945418424/11390625"
    ]
  ],
  "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 = -9914/3841. Found in a conductor-first search over reduced rational parameters using bad-reduction support filtering, Mestre-Nagao scoring, and exact PARI/GP 2-descent. PARI/GP 2.17.4 gives rank bounds [5,5] and torsion Z/6Z. ",
  "created_at": "2026-09-27 10:31:45",
  "updated_at": "2026-09-27 10:31:45"
}