Periods of quadratic twists of elliptic curves
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- by Vivek Pal; with an appendix by Amod Agashe PDF
- Proc. Amer. Math. Soc. 140 (2012), 1513-1525 Request permission
Abstract:
In this paper we prove a relation between the period of an elliptic curve and the period of its real and imaginary quadratic twists. This relation is often misstated in the literature.References
- Amod Agashe, Squareness in the special $L$-value and special $L$-values of twists, Int. J. Number Theory 6 (2010), no. 5, 1091–1111. MR 2679458, DOI 10.1142/S1793042110003393
- Amod Agashe, Kenneth Ribet, and William A. Stein, The Manin constant, Pure Appl. Math. Q. 2 (2006), no. 2, Special Issue: In honor of John H. Coates., 617–636. MR 2251484, DOI 10.4310/PAMQ.2006.v2.n2.a11
- Amod Agashe and William Stein, Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero, Math. Comp. 74 (2005), no. 249, 455–484. With an appendix by J. Cremona and B. Mazur. MR 2085902, DOI 10.1090/S0025-5718-04-01644-8
- Ian Connell, Elliptic curve handbook, preprint, available at http://www.ucm.es/ BUCM/mat/doc8354.pdf.
- Soonhak Kwon, Torsion subgroups of elliptic curves over quadratic extensions, J. Number Theory 62 (1997), no. 1, 144–162. MR 1430007, DOI 10.1006/jnth.1997.2036
- Serge Lang, Number theory. III, Encyclopaedia of Mathematical Sciences, vol. 60, Springer-Verlag, Berlin, 1991. Diophantine geometry. MR 1112552, DOI 10.1007/978-3-642-58227-1
- Ju. I. Manin, Cyclotomic fields and modular curves, Uspehi Mat. Nauk 26 (1971), no. 6(162), 7–71 (Russian). MR 0401653
- Ken Ono and Christopher Skinner, Fourier coefficients of half-integral weight modular forms modulo $l$, Ann. of Math. (2) 147 (1998), no. 2, 453–470. MR 1626761, DOI 10.2307/121015
- Joseph H. Silverman, The arithmetic of elliptic curves, Graduate Texts in Mathematics, vol. 106, Springer-Verlag, New York, 1992. Corrected reprint of the 1986 original. MR 1329092
- Joseph H. Silverman, Advanced topics in the arithmetic of elliptic curves, Graduate Texts in Mathematics, vol. 151, Springer-Verlag, New York, 1994. MR 1312368, DOI 10.1007/978-1-4612-0851-8
Additional Information
- Vivek Pal
- Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306
- Address at time of publication: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
- Email: vpal@math.fsu.edu
- Amod Agashe
- Affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306
- Received by editor(s): November 30, 2010
- Received by editor(s) in revised form: January 12, 2011, and January 15, 2011
- Published electronically: September 2, 2011
- Additional Notes: The author was funded by the FSU Office of National Fellowships
The author of the appendix was supported by National Security Agency grant No. Hg8230-10-1-0208 - Communicated by: Lev Borisov
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 1513-1525
- MSC (2010): Primary 11G05, 14H52, 11G40; Secondary 14G40
- DOI: https://doi.org/10.1090/S0002-9939-2011-11014-1
- MathSciNet review: 2869136