{
  "id": 3716,
  "curve_key": "11419512953547668170321:-1232411895571650489941817847825369",
  "ainvs": [
    "1",
    "0",
    "0",
    "-237906519865576420215",
    "1426402656891806968184602251817"
  ],
  "rank_lower_bound": 7,
  "torsion": [
    6
  ],
  "naive_height": 152.38856241771978,
  "faltings_height": 10.563269513072905,
  "conductor": "269191330439443485710",
  "bad_primes": [
    "2",
    "5",
    "7",
    "13",
    "17",
    "43",
    "53",
    "79",
    "139",
    "569",
    "1222003"
  ],
  "discriminant": "-17172650899595984038207117793077656231964053574944845824000000",
  "regulator": "56739.30484377825427389786365843319313576487286790025",
  "points": [
    [
      "247802534",
      "1169386054826773"
    ],
    [
      "34132147574",
      "5750653636612213"
    ],
    [
      "-26674500933514/2209",
      "165416647633593451739/103823"
    ],
    [
      "-141992979044/9",
      "30220234866645061/27"
    ],
    [
      "50689523549/16",
      "53717587600938387/64"
    ],
    [
      "1258430074454/121",
      "369475346358705503/1331"
    ],
    [
      "84468876807686/4489",
      "571629878379476442519/300763"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -282883/156520 of the universal curve with a 6-torsion point, y^2 + txy + (t+2)y = x^3 (as searched in arXiv:2003.00077, Sec. 13), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-30 01:48:51",
  "updated_at": "2026-09-30 01:48:51"
}