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arxiv: 1408.5650 · v3 · pith:E5EAEYMQnew · submitted 2014-08-25 · 🧮 math.NT

Generation of class fields by using the Weber function

classification 🧮 math.NT
keywords functionmathcalclassfieldweberalonecertaincomplex
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Let $K$ be an imaginary quadratic field and $\mathcal{O}_K$ be its ring of integers. Let $h_E$ be the Weber function on certain elliptic curve $E$ with complex multiplication by $\mathcal{O}_K$. We show that if $N$ ($>1$) is an integer prime to $6$, then the function $h_E$ alone generates the ray class field modulo $N\mathcal{O}_K$ over $K$ when evaluated at some $N$-torsion point of $E$.

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