The analytic order of Ш for modular elliptic curves. (English) Zbl 0795.14016

In this note some of the computations of the author’s book “Algorithms for modular elliptic curves” (Cambridge 1992; Zbl 0758.14042) are completed. The analytic order of the Tate-Shafarevich group for all curves in each isogeny class is considered there.
Reviewer: G.Pfister (Berlin)


14H52 Elliptic curves
14K02 Isogeny
11F11 Holomorphic modular forms of integral weight


Zbl 0758.14042


Full Text: DOI Numdam EuDML


[1] B. J. Birch and W. Kuyk (eds.), Modular Functions of One Variable IV, , 476, Springer-Verlag (1975). · Zbl 0315.14014
[2] Brumer, A. and McGuinness, O., The behaviour of the Mordell-Weil group of elliptic curves, Bull. AMS (New Series)23 (1990), 375-382. · Zbl 0741.14010
[3] Cassels, J.W.S., Arithmetic on curves of genus 1 (VIII). On the conjectures of Birch and Swinnerton-Dyer, J. Reine Angew. Math.217 (1965), 180-189. · Zbl 0241.14017
[4] Cremona, J.E., Algorithms for modular elliptic curves, Cambridge University Press1992. · Zbl 0758.14042
[5] Kolyvagin, V.I., Finiteness of E(Q) and IIIE/Q for a subclass of Weil curves, Math. USSR Izvest.32 (1989), 523-542. · Zbl 0662.14017
[6] Vélu, J., Isogénies entre courbes elliptiques, C. R. Acad. Sci. Paris, sér. A 273 (1971), 238-241. · Zbl 0225.14014
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.