{
  "id": 3672,
  "curve_key": "7961765106537954387913:-688642568980590360930290235466885",
  "ainvs": [
    "1",
    "0",
    "1",
    "-165870106386207383082",
    "797040010380379297766763083200"
  ],
  "rank_lower_bound": 8,
  "torsion": [
    4
  ],
  "naive_height": 151.28681302560454,
  "faltings_height": 10.523221206505513,
  "conductor": "19479441722836754745294",
  "bad_primes": [
    "2",
    "3",
    "13",
    "17",
    "29",
    "83",
    "179",
    "373",
    "863",
    "5099",
    "20773"
  ],
  "discriminant": "17630406549254631700419091666575701472304933193575111002530124",
  "regulator": "2621682.20212454681331888083268063658340443360766317617",
  "points": [
    [
      "-14271692950",
      "507364417949724"
    ],
    [
      "5863018595",
      "161495305451919"
    ],
    [
      "-23941054950493/2209",
      "119360523316926264579/103823"
    ],
    [
      "-861979603571/144",
      "2168934409983615277/1728"
    ],
    [
      "300798899906/49",
      "34536394568359188/343"
    ],
    [
      "530282983349/121",
      "522803097532696821/1331"
    ],
    [
      "584062752839/121",
      "439140330226730871/1331"
    ],
    [
      "1070405325815/121",
      "197368981706623959/1331"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 199/664 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 19:30:39",
  "updated_at": "2026-09-29 19:30:39"
}