Tom Fisher's Home Page
|
|
We compute explicit equations for the surfaces Z(17,1) and Z(17,3) parametrising pairs of 17-congruent elliptic curves. We find that each is a double cover of the same elliptic K3-surface. We use these equations to exhibit the first non-trivial example of a pair of symplectically 17-congruent elliptic curves over the rationals. We also compute the corresponding genus 2 curve whose Jacobian has a (17,17)-splitting.
