Computing the geometric endomorphism ring of a genus-2 Jacobian

  title={Computing the geometric endomorphism ring of a genus-2 Jacobian},
  author={Davide Lombardo},
  journal={Math. Comput.},
  • D. Lombardo
  • Published 2019
  • Mathematics, Computer Science
  • Math. Comput.
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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