## 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)

### MSC:

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

### Keywords:

order of the Tate-Shafarevich group; isogeny

Zbl 0758.14042

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### References:

 [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
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