Specialization at T = -2068 of the Mestre/Fermigier family y^2 = r(x,T) on the sextuple (a) = (-44, -60, -6, 110, 94, -94) [r = degree-<=4 remainder in p6(x-T)p6(x+T) = g^2-r, g monic degree 6, p6(x)=prod(x-a_i)]. Located by a Mestre-Nagao sieve of this family. Sixteen independent rational points were obtained via 2-descent covers and a direct minimal-model x = n/q^2 sieve (the extra generators are high-height on the minimal model but small on the covers); rank >= 16 follows from the positive-definiteness of their 16x16 Neron-Tate height-pairing matrix, verified independently in Sage and Magma. Conductor by Tate's algorithm. Proven lower bound on the rank (no exact-rank/Selmer/BSD claim).
Edgar Costa · 2026-06-25 21:53:06