21 citations · 21 across the 4 of their papers we have counts for
4 papers · 1 filter
Shadow line distributions
Jennifer S. Balakrishnan, Mirela Çiperiani, Barry Mazur +1
Let be an elliptic curve over with Mordell--Weil rank and be an odd prime of good ordinary reduction. For every imaginary quadratic field satisfying th…
Selmer Ranks of Quadratic Twists of Elliptic Curves with Partial Rational Two-Torsion
Zev Klagsbrun
This paper investigates which integers can appear as 2-Selmer ranks within the quadratic twist family of an elliptic curve E defined over a number field K with E(K)[2] = Z/2Z. We s…
The spin of prime ideals
J. B. Friedlander, H. Iwaniec, B. Mazur +1
Fixing a nontrivial automorphism of a number field K, we associate to ideals in K an invariant (with values in {0,1,-1}) that we call the "spin" and for which the associated L-func…
Point counting on reductions of CM elliptic curves
K. Rubin, A. Silverberg
We give explicit formulas for the number of points on reductions of elliptic curves with complex multiplication by any imaginary quadratic field. We also find models for CM $\mathb…