Generation of class fields by using the Weber function

2014/08/25 by Koo, Ja Kyung, Shin, Dong Hwa, Yoon, Dong Sung
#11G15 #11G16 #11R37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1408.5650

Abstract

Let K be an imaginary quadratic field and O_K be its ring of integers. Let h_E be the Weber function on certain elliptic curve E with complex multiplication by 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 NO_K over K when evaluated at some N-torsion point of E.

Related

• Generalised Weber Functions
• Class fields generated by coordinates of elliptic curves
• On a problem of Hasse and Ramachandra
• Ray class fields generated by torsion points of certain elliptic curves
• Certain CM class fields with smaller generators