\frametitle{Linear algebra over finite fields (Magma)}
How does the complexity of linear algebra over $\FF_{\ell}$ vary with $\ell$? A sensible behavior is exhibited by Magma 2.21-11:
\pause
\begin{verbatim}
> C := ModularSymbols(100001, 2, -1);
> M := HeckeOperator(C, 2);
> M2 := Matrix(GF(2), M); time Rank(M2);
9047
Time: 1.710
> M3 := Matrix(GF(3), M); time Rank(M3);
9085
Time: 4.220
> p := 2^30 - 35;
> Mp := Matrix(GF(p), M); time Rank(Mp);
9091
Time: 17.160
\end{verbatim}
