New curve of rank >= 20 and naive height 218.2916, beating the previous rank-20 record 223.3165 (#92). Found as the specialization T = 3895/6 of the Mestre/Fermigier rank-12 quartic family on the rational Mestre sextuple mestre_ais(u = -7/2, v = 3/2) (roots {-1455/4, 2955/4, 1437/2, -1149/4, -1851/4, -687/2}): q(x,T) = p6(x-T) p6(x+T) = g^2 - r with deg r = 4, curve = Jacobian of y^2 = r(x). Candidate surfaced by a staged Mestre-Nagao sieve (M=1500 stage 1 over T = m/n, m <= 5000, n <= 20; M=6000 rescore ranked it #1 of 3135 candidates under the rank-20 height bar, score 103.65 vs 98.36 for Fermigier's rank-22 curve in the same normalization). The 20 independent points were assembled from hyperellratpoints on the integral quartic model to height 1e7 plus the 12 injected family base points x = ai +/- T and an integer sweep ellratpoints(E, [1e12, 1]); independence certified by positive-definite Neron-Tate Gram matrix (eigenvalue margin 1e-7 at 90 digits).
David Renshaw · 2026-07-02 02:02:39