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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
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.