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Generalised Weber functions

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Enge A., Morain F.

Acta Arithmetica

2014

tom 164

nr 4

309-341

A generalised Weber function is given by $𝔴_N(z) = η(z/N)/η(z)$, where η(z) is the Dedekind function and N is any integer; the original function corresponds to N=2. We classify the cases where some power $𝔴_N^e$ evaluated at some quadratic integer generates the ring class field associated to an order of an imaginary quadratic field. We compare the heights of our invariants by giving a general formula for the degree of the modular equation relating $𝔴_N(z)$ and j(z). Our ultimate goal is the use of these invariants in constructing reductions of elliptic curves over finite fields suitable for cryptographic use.

Ograniczanie wyników

1 Acta Arithmetica

1 Enge A.

1 Morain F.

1 2014

Wyniki wyszukiwania

Generalised Weber functions