Exact rank 16, unconditional: rational 2-torsion point, 16 independent points (Neron-Tate height matrix of rank 16; the archived certificate additionally saturates the lattice at all primes up to 97 — the points listed here are the ellrank output, not the saturated basis) with matching 2-descent upper bound 16 (PARI/GP 2.15.4 ellrank, effort 3). Fiber t=-24179/8214 on branch u=38/17 of the Elkies-Klagsbrun Z/2Z rank-9 family (arXiv:2003.00077), found by a Mestre-Nagao residue-table sieve followed by an exact 2-descent-type upper bound and ellrank (Matthias Breddin, 2026-09-02; method: doi:10.5281/zenodo.22242107).
Matthias Breddin ·