Computing Low-degree Isogenies in Genus 2 with the Dolgachev–lehavi Method
نویسنده
چکیده
Let lbe a prime, andH a curve of genus 2 over a fieldkof characteristic not 2 or l. If S is amaximal Weil-isotropic subgroup ofJH [l], thenJH /S is isomorphic to the Jacobian JX of some (possibly reducible) curve X . We investigate the Dolgachev– Lehavi method for constructing the curve X , simplifying their approach and making it more explicit. The result, at least for l = 3, is an efficient and easily programmable algorithm suitable for number-theoretic calculations.
منابع مشابه
On the Arithmetic-geometric Mean for Curves of Genus 2 I. Dolgachev and D. Lehavi
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تاریخ انتشار 2013