Abstract
We study the 2-Selmer ranks of elliptic curves. We prove that for an arbitrary elliptic curve E over an arbitrary number field K, if the set AE of 2-Selmer ranks of quadratic twists of E contains an integer c, it contains all integers larger than c and having the same parity as c. We also find suficient conditions on AE such that AE is equal to Z≥tE for some number tE. When all points in E[2] are rational, we give an upper bound for tE.
Original language | English |
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Pages (from-to) | 1565-1583 |
Number of pages | 19 |
Journal | Mathematical Research Letters |
Volume | 24 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2017 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)