Computing Igusa Class Polynomials via the Chinese Remainder Theorem
نویسنده
چکیده
We present a new method for computing the Igusa class polynomials of a primitive quartic CM field. For a primitive quartic CM field, K, we compute the Igusa class polynomials modulo p for certain small primes p and then use the Chinese remainder theorem and a bound on the denominators to construct the class polynomials. We also provide an algorithm for determining endomorphism rings of Jacobians of genus 2 curves. Our algorithm can be used to generate genus 2 curves over a finite field Fn with a given zeta function.
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