{
  "id": 3681,
  "curve_key": "15679343364301461086342820015201:-61600914278309522594480580638444876502028662801",
  "ainvs": [
    "1",
    "-1",
    "1",
    "-326652986756280439298808750317",
    "71297354488784251332784398142383987320276309"
  ],
  "rank_lower_bound": 10,
  "torsion": [
    4
  ],
  "naive_height": 215.4896907797702,
  "faltings_height": 15.812005355385445,
  "conductor": "12441034926946153882022260307768910",
  "bad_primes": [
    "2",
    "3",
    "5",
    "11",
    "13",
    "17",
    "23",
    "31",
    "37",
    "47",
    "53",
    "167",
    "2591",
    "16141",
    "18911",
    "6551417"
  ],
  "discriminant": "34702249000017957985375764018401853182143737643590123594744164048166126339234201600000000",
  "regulator": "71890020.25086436490078632076921300186039244306300194839939",
  "points": [
    [
      "14961583349967",
      "8149445233517627397016"
    ],
    [
      "776823972263967",
      "16921115704804200093016"
    ],
    [
      "857105769190287",
      "20517725152225349774296"
    ],
    [
      "939992583429967",
      "24388732787266259253016"
    ],
    [
      "1439512375013967",
      "50833334280913319493016"
    ],
    [
      "1831090722272967",
      "74917405560588049278016"
    ],
    [
      "2562103395993967",
      "126700365977701273973016"
    ],
    [
      "2751534231093967",
      "141436213119256039173016"
    ],
    [
      "56533477280421967",
      "13441150332264041869125016"
    ],
    [
      "858321224143658247/841",
      "690250012202797210556607224/24389"
    ]
  ],
  "submitter": "Michael Rubinstein",
  "history": [],
  "commentary": "Specialization at t = 463/1955 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 19:32:09",
  "updated_at": "2026-09-29 19:32:09"
}