Chromatic Selmer groups and arithmetic invariants of elliptic curves

The Iwasawa invariants of the plus/minus Selmer groups of elliptic curves for supersingular primes

We study the Iwasawa μand λ-invariants of the plus/minus Selmer groups of elliptic curves with the same residual representation using the ideas of [8]. As a result we find a family of elliptic curves whose plus/minus Selmer groups have arbitrarily large λ-invariants.

Symmetric Squares of Elliptic Curves: Rational Points and Selmer Groups

Average Size of 2-selmer Groups of Elliptic Curves, I

In this paper, we study a class of elliptic curves over Q with Qtorsion group Z2×Z2, and prove that the average order of the 2-Selmer groups is bounded.

Selmer Groups of Quadratic Twists of Elliptic Curves

(1.1) E : y + a1xy + a3y = x + a2x + a4x+ a6 where a1, a2, a3, a4, a6 ∈ Z. Let N(E) denote the conductor of E, j(E) the j-invariant of E, and L(E, s) = ∑∞ n=1 a(n)n −s the Hasse-Weil L-function of E. If E is modular, then let FE(z) = ∑∞ n=1 aE(n)q n ∈ S2(N(E), χ1) be the associated weight 2 cusp form. Here χ1 denotes the trivial Dirichlet character. Throughout, D will denote a square-free integ...

2-selmer Groups of Quadratic Twists of Elliptic Curves

In this paper we investigate families of quadratic twists of elliptic curves. Addressing a speculation of Ono, we identify a large class of elliptic curves for which the parities of the “algebraic parts” of the central values L(E/Q, 1), as d varies, have essentially the same multiplicative structure as the coefficients ad of L(E/Q, s). We achieve this by controlling the 2-Selmer rank (à la Mazu...