Class fields generated by coordinates of elliptic curves
Class fields generated by coordinates of elliptic curves
Abstract Let <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>K</m:mi> </m:math> K be an imaginary quadratic field different from <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi mathvariant="double-struck">Q</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msqrt> <m:mrow> <m:mo>−</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msqrt> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {\mathbb{Q}}\left(\sqrt{-1}) and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi mathvariant="double-struck">Q</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msqrt> <m:mrow> <m:mo>−</m:mo> <m:mn>3</m:mn> </m:mrow> </m:msqrt> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> …