On the Mordell--Weil lattice of $y^2=x^3+bx+t^{3^n+1}$ in characteristic $3$

Gauthier Leterrier

We study the elliptic curves given by $y^2=x^3+bx+t^{3^n+1}$ over global function fields of characteristic $3$; in particular we perform an explicit computation of the $L$-f…