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Class invariants by the CRT method

Abstract : We adapt the CRT approach for computing Hilbert class polynomials to handle a wide range of class invariants. For suitable discriminants $D$, this improves its performance by a large constant factor, more than 200 in the most favourable circumstances. This has enabled record-breaking constructions of elliptic curves via the CM method, including examples with $|D|>10^{15}$.
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Contributor : Andreas Enge Connect in order to contact the contributor
Submitted on : Saturday, May 1, 2010 - 3:33:06 PM
Last modification on : Saturday, December 4, 2021 - 3:42:36 AM
Long-term archiving on: : Thursday, September 23, 2010 - 12:31:20 PM


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Andreas Enge, Andrew Sutherland. Class invariants by the CRT method. Ninth Algorithmic Number Theory Symposium ANTS-IX, Jul 2010, Nancy, France. pp.142-156, ⟨10.1007/978-3-642-14518-6_14⟩. ⟨inria-00448729v2⟩



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