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arXiv · 1408.5650

Generation of class fields by using the Weber function

Ja Kyung Koo·Dong Hwa Shin·Dong Sung Yoon
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Abstract

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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Ja Kyung Koo, Dong Hwa Shin, Dong Sung Yoon. 2014-08-25. Generation of class fields by using the Weber function. https://arxiv.org/abs/1408.5650

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