论一类Q曲线的基本算术性质

ON SOME BASIC ARITHMETIC PROPERTIES OF A CLASS OF Q-CURVES

摘要:

在本文中，对任意模4余3的正整数D，我们将构造一类以判别式为-D的虚二次域的整数环为复乘的椭圆曲线。进而，我们将考察其基本性质，比如有理扭点，自同态环以及模性等.

Abstract:

In this paper, we construct elliptic curves with complex multiplications by the integer ring of the quadratic imaginary field of discriminant -D for any positive integer D congruent to 3 modulo 4 and establish their basic properties. Our results generalize those of Gross.