DIOPHANTINE EQUATIONS AND MODULAR FORMS
DIOPHANTINE EQUATIONS AND MODULAR FORMS
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DOI：
10.1090/s0002-9904-1975-13623-8
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发表时间：
1975-01-01
影响因子：
1.3
通讯作者：
OGG, AP
中科院分区：
文献类型：
--
作者：
OGG, AP
(1)E：y2= 4x*-g2 x-gz，其中g2，g3 e K; E是非奇异的意味着判别式A= g1 - 27 g1不是0。（在特征2或3中需要稍微修改的三次方程。）E有一个自然群律，写为加法，无穷远处的唯一点0=（oo，oo）为零，定义为E上的三个点相加为0当且仅当它们共线。E则是定义在K上的维数为1的阿贝尔簇。设E（K）表示E中坐标在K中的点的群。
(1) E: y2= 4x*-g2x-gz, where g2, g3 e K; that E is nonsingular means that the discriminant A= gl—27gl is not 0.(A slightly modified cubic equation is required in characteristic 2 or 3.) E has a natural group law, written additively, with the unique point at infinity, 0=(oo, oo), as zero, defined by the rule that three points on E add up to 0 if and only if they are collinear. E is then an abelian variety of dimension 1 defined over K. Let E (K) denote the group of points of E with coordinates in K.