Found on 2026-09-19 by searching a second elliptic fibration of the D=26 K3 companion at moduli parameter j=4. The source equation is Y^2=X^3+t^3(352836-552123t)X-t^5(323554257+158153580t+729t^2). Setting u=X/t^2 gives a rational-2-torsion pencil; this curve is its fiber u=225/4 (scaled parameter v=-75/4). Candidates were selected by a Mestre-Nagao prime-sum sieve through 251 on a reduced-rational box |numerator(v)|<=256, denominator(v)<=8, then examined in Magma. A GRH-assisted descent found the seven submitted points. In a fresh process with rigorous Minkowski class-group bounds, exact point identities and IsLinearlyIndependent verified their independence modulo torsion, proving rank >=7 unconditionally. The computed upper bound 7 remains GRH-conditional; no saturated-basis claim is made. Magma also verified global minimality, torsion Z/2, and conductor 47048397659668784440854. The exact map back to the source K3 is t=-(x+112019271)/1296, X=(225/4)t^2, Y=(2y+x+1)t^2/3456.
benvchurch ·