\begin{table}[!ht] \centering\small \begin{tabular}{rrrrrl} \toprule rank & curves & optimal & fixed & only optimal & median ratio\\ \midrule 24 & 55 & 55 & 55 & 0 & 3.1\\ 25 & 65 & 65 & 65 & 0 & 3.6\\ 26 & 43 & 43 & 43 & 0 & 3.6\\ 27 & 44 & 43 & 43 & 0 & 4.1\\ 28 & 87 & 76 & 74 & 2 & 4.2\\ 29 & 50 & 50 & 47 & 3 & 4.7\\ 30 & 34 & 34 & 33 & 1 & 5.3\\ 31 & 17 & 13 & 12 & 1 & 6.9\\ \midrule all & 395 & 379 & 372 & 7 & 4.0\\ \bottomrule \end{tabular} \caption{ICARM curves of rank $24$--$31$: number of curves on which each kernel certifies $\ran\le r$ under GRH with $p<10^{10}$; ``only optimal'' = certified by the optimal kernel but not by the fixed one; ratio = primes needed by the fixed kernel divided by primes needed by the optimal kernel, over curves where both succeed.} \label{tab:board} \end{table}