Fast algorithms for computing isogenies between elliptic curves
<|reference_start|>Fast algorithms for computing isogenies between elliptic curves: We survey algorithms for computing isogenies between elliptic curves defined over a field of characteristic either 0 or a large prime. We introduce a new algorithm that computes an isogeny of degree $\ell$ ($\ell$ different from the characteristic) in time quasi-linear with respect to $\ell$. This is based in particular on fast algorithms for power series expansion of the Weierstrass $\wp$-function and related functions.<|reference_end|>
@article{bostan2006fast,
    title={Fast algorithms for computing isogenies between elliptic curves},
    author={Alin Bostan (INRIA Rocquencourt), Bruno Salvy (INRIA Rocquencourt),
  Francois Morain (LIX, INRIA Futurs), Eric Schost (LIX)},
    journal={arXiv preprint arXiv:cs/0609020},
    year={2006},
    doi={10.1090/S0025-5718-08-02066-8},
    archivePrefix={arXiv},
    eprint={cs/0609020},
    primaryClass={cs.CC cs.SC math.NT}
}