Supersingular primes for elliptic curves over real number fields. (English) Zbl 0708.14020

Let \(E\) be an elliptic curve defined over a number field \(K\). The author proved in an earlier paper [Invent. Math. 89, No. 3, 561–567 (1987; Zbl 0631.14024)] that if \([K:\mathbb Q]\) is odd then \(E\) has infinitely many primes of supersingular reduction. This is generalized in the present article by showing that the same result holds if \(K\) has at least one real embedding.


11G05 Elliptic curves over global fields
14G25 Global ground fields in algebraic geometry


Zbl 0631.14024
Full Text: Numdam EuDML


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