On the signed Selmer groups of congruent elliptic curves with semistable reduction at all primes above $p$

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.

Selmer Groups and Torsion Zero Cycles on the Selfproduct of a Semistable Elliptic Curve

In this paper we extend the niteness result on the p-primary torsion subgroup in the Chow group of zero cycles on the selfproduct of a semistable elliptic curve obtained in joint work with S. Saito to primes p dividing the conductor. On the way we show the niteness of the Selmer group associated to the symmetric square of the elliptic curve for those primes. The proof uses p-adic techniques, in...

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...

Symmetric Squares of Elliptic Curves: Rational Points and Selmer Groups