scholarly journals On class numbers, torsion subgroups, and quadratic twists of elliptic curves

2021 ◽  
pp. 1
Author(s):  
Talia Blum ◽  
Caroline Choi ◽  
Alexandra Hoey ◽  
Jonas Iskander ◽  
Kaya Lakein ◽  
...  
Keyword(s):  
Elliptic Curves ◽  
Class Numbers ◽  
Quadratic Twists ◽  
Torsion Subgroups

scholarly journals Disparity in Selmer ranks of quadratic twists of elliptic curves

2013 ◽  
Vol 178 (1) ◽  
pp. 287-320 ◽  
Author(s):  
Zev Klagsbrun ◽  
Barry Mazur ◽  
Karl Rubin
Keyword(s):  
Elliptic Curves ◽  
Quadratic Twists

scholarly journals ON SELMER RANK PARITY OF TWISTS

2016 ◽  
Vol 102 (3) ◽  
pp. 316-330 ◽  
Author(s):  
MAJID HADIAN ◽  
MATTHEW WEIDNER
Keyword(s):  
Elliptic Curves ◽  
Abelian Variety ◽  
Number Field ◽  
Arbitrary Number ◽  
Hyperelliptic Curve ◽  
Abelian Varieties ◽  
Hyperelliptic Curves ◽  
Torsion Subgroup ◽  
Tate Conjecture ◽  
Quadratic Twists

In this paper we study the variation of the $p$-Selmer rank parities of $p$-twists of a principally polarized Abelian variety over an arbitrary number field $K$ and show, under certain assumptions, that this parity is periodic with an explicit period. Our result applies in particular to principally polarized Abelian varieties with full $K$-rational $p$-torsion subgroup, arbitrary elliptic curves, and Jacobians of hyperelliptic curves. Assuming the Shafarevich–Tate conjecture, our result allows one to classify the rank parities of all quadratic twists of an elliptic or hyperelliptic curve after a finite calculation.

scholarly journals Ranks of Elliptic Curves in Families of Quadratic Twists

2000 ◽  
Vol 9 (4) ◽  
pp. 583-590 ◽  
Author(s):  
Karl Rubin ◽  
Alice Silverberg
Keyword(s):  
Elliptic Curves ◽  
Quadratic Twists

scholarly journals Elliptic curves, modular forms, and sums of Hurwitz class numbers

2008 ◽  
Vol 128 (6) ◽  
pp. 1847-1863 ◽  
Author(s):  
Brittany Brown ◽  
Neil J. Calkin ◽  
Timothy B. Flowers ◽  
Kevin James ◽  
Ethan Smith ◽  
...  
Keyword(s):  
Elliptic Curves ◽  
Modular Forms ◽  
Class Numbers

scholarly journals Moments and distribution of central $$L$$ L -values of quadratic twists of elliptic curves

2015 ◽  
Vol 202 (3) ◽  
pp. 1029-1068 ◽  
Author(s):  
Maksym Radziwiłł ◽  
K. Soundararajan
Keyword(s):  
Elliptic Curves ◽  
Quadratic Twists

scholarly journals Quadratic twists of elliptic curves

2014 ◽  
Vol 110 (2) ◽  
pp. 357-394 ◽  
Author(s):  
John Coates ◽  
Yongxiong Li ◽  
Ye Tian ◽  
Shuai Zhai
Keyword(s):  
Elliptic Curves ◽  
Quadratic Twists

scholarly journals Selmer groups of quadratic twists of elliptic curves

1999 ◽  
Vol 314 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Kevin James ◽  
Ken Ono
Keyword(s):  
Elliptic Curves ◽  
Selmer Groups ◽  
Quadratic Twists
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