Modular Elliptic Curves over Q(5) - William Stein
Modular Elliptic Curves over Q(5) - William Stein
Modular Elliptic Curves over Q(5) - William Stein
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
<strong>Curves</strong> <strong>over</strong><br />
Q( √ 5)<br />
W. <strong>Stein</strong><br />
Background<br />
The Plan<br />
Computing Hilbert <strong>Modular</strong> Forms<br />
Overview of Dembele’s Algorithm<br />
1 Let R = maximal order in Hamilton quaternion algebra<br />
<strong>over</strong> F = Q( √ 5).<br />
2 Compute the finite set S = R ∗ \P 1 (OF /n). Let X = free<br />
abelian group on S.<br />
3 To compute the Hecke operator Tp on X , compute (and<br />
store once and for all) #Fp + 1 elements αp,i ∈ B with<br />
norm p, then compute<br />
Tp(x) = αp,i(x).<br />
That’s it! Now scroll through the 1500 line file I wrote yesterday<br />
that implements this in many cases... but still isn’t done.<br />
Deines-<strong>Stein</strong>: article about how to do 2-3 above quickly?
Change language