We study the ramifications in the extensions of number fields arising from an isogeny of elliptic curves. In particular, we start with an elliptic curve with a rational torsion point, and show that the extension is unramified if and "only if" the point which generates the extension is reduced into a nonsingular point (we need to assume certain conditions in order to prove the "only if" part). We also study a characterization of quadratic number fields with class numbers divisible by 5.
|Number of pages||18|
|Journal||Osaka Journal of Mathematics|
|Publication status||Published - 2011 Sep 1|
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