{
  "id": 3669,
  "curve_key": "324955972529474673025:-8322850207492594338783068518625",
  "ainvs": [
    "1",
    "1",
    "1",
    "-6769916094364055688",
    "9632928478073408037976861656"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4
  ],
  "naive_height": 142.39311511801137,
  "faltings_height": 9.89038936703637,
  "conductor": "7107840925923552917025",
  "bad_primes": [
    "3",
    "5",
    "7",
    "11",
    "19",
    "101",
    "239",
    "251",
    "311",
    "5519",
    "6229"
  ],
  "discriminant": "-20228969844450156501638865914449837700655219218099132109375",
  "regulator": "94303232.1646513097911848343000766350800731274740749780",
  "points": [
    [
      "-3131394160",
      "11267160209367"
    ],
    [
      "-2600315810",
      "98258325017717"
    ],
    [
      "227934949831/169",
      "119438976869482964/2197"
    ],
    [
      "1371356051710/1849",
      "5633104990308653444/79507"
    ],
    [
      "4988400305335/1849",
      "8340682468870875644/79507"
    ],
    [
      "171133089049435/124609",
      "2379219832253811182434/43986977"
    ],
    [
      "14924346015677370/18241441",
      "5307944609064001358472372/77909194511"
    ],
    [
      "959611202914621660/506565049",
      "684665723564248482120273656/11401259557843"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 3/502 of the Elkies-Klagsbrun Z/4 fibration E1: y^2 + a*xy + a*c*y = x^3 + c*x^2, a = (8t-1)(32t+7), c = 8(t+1)(15t-8)(31t-7) (arXiv:2003.00077, eq. (5)), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).",
  "created_at": "2026-09-29 19:30:08",
  "updated_at": "2026-09-29 19:30:08"
}