Inversion of the $j$--function and testing complex multiplication
John Armitage
TL;DR
This paper presents a fast algorithm for inverting the $j$--function and applies it to efficiently test whether elliptic curves possess complex multiplication, advancing computational number theory methods.
Contribution
The authors introduce a quasilinear time algorithm for inverting the $j$--function and demonstrate its application in testing complex multiplication of elliptic curves.
Findings
Algorithm operates in quasilinear time
Enables efficient testing of complex multiplication
Improves computational methods in elliptic curve analysis
Abstract
We develop an algorithm to invert the --function in quasilinear time, and apply this to testing whether an elliptic curve has complex multiplication.
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Taxonomy
TopicsCryptography and Residue Arithmetic · Algebraic Geometry and Number Theory · Analytic Number Theory Research