Let E/k be an elliptic curve with CM by O. We determine a formula for (a generalization of) the arithmetic local constant of Mazur-Rubin at almost all primes of good reduction. We apply this formula to the CM curves defined over Q and are able to describe extensions F/Q over which the O-rank of E grows.
Copyright © 2014 Rocky Mountain Mathematics Consortium
Chetty S, Li L. 2014. Computing local constants for CM elliptic curves. Rocky Mountain Journal of Mathematics 44(3): 853-863.