# Computing the geometric endomorphism ring of a genus-2 Jacobian

@article{Lombardo2019ComputingTG, title={Computing the geometric endomorphism ring of a genus-2 Jacobian}, author={Davide Lombardo}, journal={Math. Comput.}, year={2019}, volume={88}, pages={889-929} }

We describe an algorithm, based on the properties of the characteristic polynomials of Frobenius, to compute $\operatorname{End}_{\overline{K}}(A)$ when $A$ is the Jacobian of a nice genus-2 curve over a number field $K$. We use this algorithm to confirm that the description of the structure of the geometric endomorphism ring of $\operatorname{Jac}(C)$ given in the LMFDB ($L$-functions and modular forms database) is correct for all the genus 2 curves $C$ currently listed in it. We also discuss… Expand

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