Found by specializing Noam D. Elkies's rank-17 elliptic K3 fibration (arXiv:2608.25406) at t = 28/117. The 6 points beyond the seventeen generic sections come from the surface's rational quadratic sections: writing x_tau = a/c^2 and y_tau = b/c^3 for a trace of height 10, the slope of the bisection is forced to be kappa/c with kappa = -b*a^(-1) mod c^2 of degree 5, so each section's point on this fibre is obtained by one polynomial evaluation and one square test rather than by any search. Claimed lower bound: rank >= 23.
Bhavik Mehta ·