On the splitting of primes in $K(E[n])$

Mathematics – Number Theory

Scientific paper

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8 pages

Scientific paper

We underline the role that Hilbert Class Polynomials play in the
decomposition of primes in torsion fields arising from elliptic curves $E$ over
certain "small" number fields $K$. The main result is a reciprocity law for
$K(E[n])/K$, where $K$ has degree $\leq 2$ over $\qu$, and where $n>2$.

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