Explicit identities for invariants of elliptic curves
Explicit identities for invariants of elliptic curves
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DOI：
10.1016/j.jnt.2005.12.008
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发表时间：
2006-10
影响因子：
0.7
通讯作者：
P. Morton
中科院分区：
文献类型：
--
作者：
P. Morton
给出了椭圆曲线E在特征p上的超奇异多项式ssp（t）和Hasse不变量H p（E）的新的显式公式，并利用这些公式导出了具有n阶特征点的椭圆曲线Enin Tate标准形的Hasse不变量的恒等式.这证明了H（E4）和H（E5）分别是八面体群和二十面体群的射影不变量（mod p）;以及勒让德规范形Y2=X（X−1）（X−λ）在特征p中的超奇异参数的四次方根λ1/4的集合具有八面体对称性。对一般n ∈ 4，确定了超奇异En的定义域，沿着确定了En上n阶点的定义域.
New explicit formulas are given for the supersingular polynomial ssp(t) and the Hasse invariant Hˆp(E) of an elliptic curve E in characteristic p. These formulas are used to derive identities for the Hasse invariants of elliptic curves Enin Tate normal form with distinguished points of order n. This yields a proof that Hˆ(E4) and Hˆ(E5) are projective invariants (mod p) for the octahedral group and the icosahedral group, respectively; and that the set of fourth roots λ1/4of supersingular parameters of the Legendre normal form Y2=X(X−1)(X−λ) in characteristic p has octahedral symmetry. For general n⩾4, the field of definition of a supersingular Enis determined, along with the field of definition of the points of order n on En.