E has trivial torsion and rank at least 32. It is the fibre at t = -248188/1981293 of a rank-17 elliptic K3 surface (the same surface as #4239). Assuming GRH, a Selmer-group bound computed with conditional class groups gives rank at most 32, so the rank is exactly 32 under GRH.
Found by a collaboration between:
Blair Butler, Lewis Combes, Shir Levav-Porat
Search performed by Claude code Opus 5.5
Lewis Combes ·