On isogenies among certain abelian varieties
2019
Using elliptically fibered Kummer surfaces of Picard rank 17, we construct an explicit model for a three-parameter bielliptic plane genus-three curve whose associated Prym variety is two-isogenous to the Jacobian variety of the general three-parameter hyperelliptic genus-two curve in Rosenhain normal form. Our model provides explicit expressions for all coefficients in terms of modular forms.
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