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Computing low-degree isogenies in genus 2 with the Dolgachev–Lehavi method
[unknown]
2012
Contemporary Mathematics
unpublished
Preserved Fulltext
Let ℓ be a prime, and H a curve of genus 2 over a field k of characteristic not 2 or ℓ. If S is a maximal Weil-isotropic subgroup of J H [ℓ], then J H /S is isomorphic to the Jacobian J X 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. 2010 Mathematics
doi:10.1090/conm/574/11418
fatcat:kqt7msicyrbsho6des4kxr276m