We computed special values of twists of the custom written papers congruent number curve by computing a weight 3/2 modular form as the product of three theta series. The previous record was 2\cdot 10^{10} coefficients of this modular form (which has a sparsity of 8), which we can do in about 30 minutes and we agree with the formerly computed data.
We are aiming for 10^{12} coefficients, and have successfully multiplied polynomials of size 10^{11}. Input of this size (325GB) does not all fit into RAM on any machine we have, so we have a custom multiply algorithm that uses the disk. The computation is currently running and is expected to finish by the time we reach our respective destinations.
Rough code is up at http://sage.math.washington.edu/home/robertwb/disk_mul/
Update
The code now works, though is still inoptimal (reading too many small pieces of data from disk). * Preliminary results for 3 mod 8 class up to 10^{12}: 869015848 squarefree congruent numbers.
This took about 2 real days, a maximum of 83GB of memory at any time, and between 2-3TB of disk space. Maximal thread usage was 6 threads (plus one for I/O), though during the FFT/IFFT stages, it was only 2 threads, I think.
Bill and Gonzalo will likely verify this result soon. We will also spot-check the results.
We will progress to 1 mod 8, 2 mod 16, and 10 mod 16, and possibly a similar problem involving class numbers.