## 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.

### MSC:

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

Zbl 0631.14024
Full Text:

### References:

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