Cremona, J. E. and Thongjunthug, Thotsaphon (2010) The complex AGM, periods of elliptic curves over C and complex elliptic logarithms. Working Paper. ArXiv e-prints. ArXiv e-prints (No.1011.0914v1).

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Abstract

We present a method for computing period lattices and elliptic logarithms for elliptic curves defined over C, using the complex Arithmetic-Geometric Mean (AGM) first studied by Gauss. Earlier authors have only considered the case of elliptic curves defined over the real numbers; here, the multi-valued nature of the complex AGM plays an important role. Our method, which we have implemented in both MAGMA and Sage, is illustrated with several examples.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Series Name:	ArXiv e-prints
Publisher:	ArXiv e-prints
Official Date:	3 November 2010
Dates:	Date Event 3 November 2010 ["eprint_fieldopt_dates_date_type_available" not defined]
Number:	No.1011.0914v1
Number of Pages:	31
Institution:	University of Warwick
Status:	Not Peer Reviewed
Publication Status:	Published
Related URLs:	http://arxiv.org/abs/1011.0914

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