Showing 1999Show all
3 papers · 1 filter
math.NT1999
Ranks of elliptic curves in families of quadratic twists
Karl Rubin, Alice Silverberg
We show that the unboundedness of the ranks of the quadratic twists of an elliptic curve is equivalent to the divergence of certain infinite series.
math.NT1999
Polarizations on abelian varieties and self-dual ell-adic representations of inertia groups
Alice Silverberg, Yuri G. Zarhin
It is well-known that every finite subgroup of GL_d(Q_{\ell}) is conjugate to a subgroup of GL_d(Z_{\ell}). However, this does not remain true if we replace general linear groups b…
math.NT1999
Mod 2 representations of elliptic curves
Karl Rubin, Alice Silverberg
This note gives explicit equations for the elliptic curves (in characteristic not 2 or 3) with mod 2 representation isomorphic to that of a given one.