# The analytic order of III for modular elliptic curves

Journal de théorie des nombres de Bordeaux (1993)

- Volume: 5, Issue: 1, page 179-184
- ISSN: 1246-7405

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topCremona, J. E.. "The analytic order of III for modular elliptic curves." Journal de théorie des nombres de Bordeaux 5.1 (1993): 179-184. <http://eudml.org/doc/93571>.

@article{Cremona1993,

abstract = {In this note we extend the computations described in [4] by computing the analytic order of the Tate-Shafarevich group III for all the curves in each isogeny class ; in [4] we considered the strong Weil curve only. While no new methods are involved here, the results have some interesting features suggesting ways in which strong Weil curves may be distinguished from other curves in their isogeny class.},

author = {Cremona, J. E.},

journal = {Journal de théorie des nombres de Bordeaux},

keywords = {order of the Tate-Shafarevich group; isogeny},

language = {eng},

number = {1},

pages = {179-184},

publisher = {Université Bordeaux I},

title = {The analytic order of III for modular elliptic curves},

url = {http://eudml.org/doc/93571},

volume = {5},

year = {1993},

}

TY - JOUR

AU - Cremona, J. E.

TI - The analytic order of III for modular elliptic curves

JO - Journal de théorie des nombres de Bordeaux

PY - 1993

PB - Université Bordeaux I

VL - 5

IS - 1

SP - 179

EP - 184

AB - In this note we extend the computations described in [4] by computing the analytic order of the Tate-Shafarevich group III for all the curves in each isogeny class ; in [4] we considered the strong Weil curve only. While no new methods are involved here, the results have some interesting features suggesting ways in which strong Weil curves may be distinguished from other curves in their isogeny class.

LA - eng

KW - order of the Tate-Shafarevich group; isogeny

UR - http://eudml.org/doc/93571

ER -

## References

top- [1] B. J. Birch and W. Kuyk (eds.), Modular Functions of One Variable IV, Lecture Notes in Mathematics, 476, Springer-Verlag (1975). Zbl0315.14014MR376533
- [2] A. Brumer and O. McGuinness, The behaviour of the Mordell-Weil group of elliptic curves, Bull. AMS (New Series)23 (1990), 375-382. Zbl0741.14010MR1044170
- [3] J.W.S. Cassels, Arithmetic on curves of genus 1 (VIII). On the conjectures of Birch and Swinnerton-Dyer, J. Reine Angew. Math.217 (1965), 180-189. Zbl0241.14017MR179169
- [4] J.E. Cremona, Algorithms for modular elliptic curves, Cambridge University Press1992. Zbl0758.14042MR1201151
- [5] V.I. Kolyvagin, Finiteness of E(Q) and IIIE/Q for a subclass of Weil curves, Math. USSR Izvest.32 (1989), 523-542. Zbl0662.14017MR954295
- [6] J. Vélu, Isogénies entre courbes elliptiques, C. R. Acad. Sci. Paris, sér. A273 (1971), 238-241. Zbl0225.14014MR294345

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