13 citations · 13 across the 2 of their papers we have counts for
5 papers
The main conjecture for CM elliptic curves at supersingular primes
Robert Pollack, Karl Rubin
At a prime of ordinary reduction, the Iwasawa ``main conjecture'' for elliptic curves relates a Selmer group to a -adic -function. In the supersingular case, the statement of…
Elliptic curves and class field theory
Barry Mazur, Karl Rubin
Suppose is an elliptic curve defined over $\Q$. At the 1983 ICM the first author formulated some conjectures that propose a close relationship between the explicit class field…
Rank frequencies for quadratic twists of elliptic curves
Karl Rubin, Alice Silverberg
We give explicit examples of infinite families of elliptic curves E over Q with (nonconstant) quadratic twists over Q(t) of rank at least 2 and 3. We recover some results announced…
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.
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.