1000 curves E: Y^2 = X(X+U^4)(X+V^4), U=m^2-n^2, V=2mn, W=m^2+n^2, 1000 < m <= 2000, gcd(m,n)=1, m-n odd.
No anti-Sha condition. Filters: parity number t even; 2-Selmer bound (full 2-descent, our code) >= 4 on E, on E': Y^2=X(X+W^4)(X+(V^2-U^2)^2), and on F: Y^2=X(X-u^4)(X-v^4), u=V+U, v=V-U.
group = top: the 500 survivors with the largest Mestre-Nagao sum (5<=p<=600) among 7000 even-t curves of largest sum;
group = rnd: 500 survivors drawn at random (seed fixed) from the remaining ~297 000 even-t curves.
Column nagao_S_p600 = sum over 5<=p<=600 of -a_p log(p)/p. For calibration our ten rank-3 records have S between 1.83 and 7.97.
