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- W2739778811 abstract "This work builds on earlier results. We define universal elliptic Gau{ss} sums for Atkin primes in Schoof's algorithm for counting points on elliptic curves. Subsequently, we show these quantities admit an efficiently computable representation in terms of the $j$-invariant and two other modular functions. We analyse the necessary computations in detail and derive an alternative approach for determining the trace of the Frobenius homomorphism for Atkin primes using these pre-computations. A rough run-time analysis shows, however, that this new method is not competitive with existing ones." @default.
- W2739778811 created "2017-08-08" @default.
- W2739778811 creator A5068390563 @default.
- W2739778811 date "2017-07-28" @default.
- W2739778811 modified "2023-09-27" @default.
- W2739778811 title "Universal elliptic Gau{ss} sums for Atkin primes in Schoof's algorithm" @default.
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