%A SUN Nai-zhe
%T Criterion for Elliptic Curves with the Lowest 3-Power in *L*(1)(Chinese)
%0 Journal Article
%D 2007
%J Journal of East China Normal University(Natural Science)
%R
%P 12-19
%V 2007
%N 5
%U {https://xblk.ecnu.edu.cn/CN/abstract/article_24250.shtml}
%8 2007-09-25
%X Let* K* be the 3^{rd} cyclotomic field, E _{D}^{[lambda]} :y^{2}=x^{3}-2^{4} 3 ^{3} D^{[lambda]] }be an elliptic curve defined over *K*, where D\in K is a square-free algebraic integer and [[lambda]] in Z . Qiu Derong found a rather complicated function as the criterion for the value of the Hecke *L*-function attached to the curve E _{D}^{[lambda]}([lambda]=2,4) at s=1 divided by the period [OMEGA] to be exactly divisible by 3 ^{n/2 -1} . This paper reduced Qiu’s criterion to a simpler version in terms of weighted graphs.