{
  "id": 3709,
  "curve_key": "324511530589270144:-185492941736695255020312928",
  "ainvs": [
    "0",
    "1",
    "0",
    "-6760656887276461",
    "214690902534289434588764"
  ],
  "rank_lower_bound": 6,
  "torsion": [
    6
  ],
  "naive_height": 120.97011812648744,
  "faltings_height": 7.90106218608923,
  "conductor": "21175657519450980",
  "bad_primes": [
    "2",
    "3",
    "5",
    "7",
    "13",
    "19",
    "23",
    "29",
    "59",
    "1979",
    "2621"
  ],
  "discriminant": "-135450033508050952180840901239018335036218132400",
  "regulator": "5428.8480436150140651930515375267752948462494879741",
  "points": [
    [
      "-8452951",
      "520801709415"
    ],
    [
      "21464924",
      "281893116960"
    ],
    [
      "69337229",
      "281558010825"
    ],
    [
      "196273181/4",
      "265162695525/8"
    ],
    [
      "377806936/9",
      "1882827141650/27"
    ],
    [
      "495136876/9",
      "2598883241500/27"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = -21608/11571 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 01:47:28",
  "updated_at": "2026-09-30 01:47:28"
}