Access the full text.
Sign up today, get DeepDyve free for 14 days.
K. Hulek (1986)
Projective geometry of elliptic curves
J. Cremona, B. Mazur (2000)
Visualizing Elements in the Shafarevich—Tate GroupExperimental Mathematics, 9
D. Mumford (1967)
On the equations defining abelian varieties. IIIInventiones mathematicae, 3
(1997)
Algorithms for modular elliptic curves (second edition)
M. Delong (1999)
A formula for the Selmer group of a rational three-isogenyActa Arithmetica, 105
B. Mazur (1993)
On the Passage From Local to Global in Number TheoryBulletin of the American Mathematical Society, 29
K. Kramer (1983)
A family of semistable elliptic curves with large Tate-Shafarevitch groups, 89
(1999)
O’Neil: Jacobians of curves of genus one
J. Cassels (1991)
Lectures on elliptic curves
F. Klein (1878)
Ueber die Transformation siebenter Ordnung der elliptischen FunctionenMathematische Annalen, 14
J. Silverman (1994)
Advanced Topics in the Arithmetic of Elliptic Curves
J. Cassels (1964)
Arithmetic on Curves of genus 1. VI. The Tate-Safarevic group can be arbitrarily large.Journal für die reine und angewandte Mathematik (Crelles Journal), 1964
J. Milne (1987)
Arithmetic Duality Theorems
S. Levy (2002)
The Eightfold way : the beauty of Klein's quartic curveThe Mathematical Gazette, 86
J. Igusa (1972)
Equations Defining Abelian Varieties
P. Monsky (1996)
Generalizing the Birch–Stephens theorem I. Modular curvesMathematische Zeitschrift, 221
J. Cassels (1965)
Arithmetic on curves of genus 1. VIII. On conjectures of Birch and Swinnerton-Dyer.Journal für die reine und angewandte Mathematik (Crelles Journal), 1965
David Rohrlich (1993)
Variation of the root number in families of elliptic curvesCompositio Mathematica, 87
B. Mazur (1986)
Arithmetic on curvesBulletin of the American Mathematical Society, 14
Jean-Pierre Serre (1971)
Propriétés galoisiennes des points d'ordre fini des courbes elliptiquesInventiones mathematicae, 15
I. Connell (1994)
Calculating root numbers of elliptic curves over Qmanuscripta mathematica, 82
We perform descent calculations for the families of elliptic curves over Q with a rational point of order n = 5 or 7. These calculations give an estimate for the Mordell-Weil rank which we relate to the parity conjecture. We exhibit explicit elements of the Tate-Shafarevich group of order 5 and 7, and show that the 5-torsion of the Tate-Shafarevich group of an elliptic curve over Q may become arbitrarily large.
Journal of the European Mathematical Society – Springer Journals
Published: May 1, 2001
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.