Specialization at T = -2407/2 of the Mestre/Fermigier family y^2 = r(x,T), where r is the degree-<=4 remainder in p6(x-T)*p6(x+T) = g(x)^2 - r (g monic of degree 6), p6(x) = prod_i(x-a_i) on the sextuple (a) = (-44, -60, -6, 110, 94, -94). Located by a Mestre-Nagao sieve of this family for small-conductor high-rank specializations. Seventeen independent rational points were found by rational-x enumeration on the quartic plus a direct minimal-model x = n/q^2 sieve; rank >= 17 follows from the positive-definiteness of their 17x17 Neron-Tate height-pairing matrix, computed independently in Sage and Magma. Conductor by Tate's algorithm. Proven lower bound on the Mordell-Weil rank (no exact-rank, Selmer, or BSD claim).
Edgar Costa · 2026-06-25 21:52:44