Classification of generalized weierstrass form Elliptic Curves Over Z_n

Computational results for classification of Elliptic Curves are demonstrated via this HTML page. Results are obtained using C++ program and then converted into HTML tables.

Elliptic Curves over Z_n

Generalized weierstrass equation for elliptic curves are given by $\mathbf{y^2+a_1 x y+a_3 y=x^3+a_2 x^2+a_4 x+a_6}$ , where $\mathbf{a_i \in \mathbb{Z}_n}$ . Discriminant ( $\mathbf{\Delta}$ ) for elliptic curve is given by,

$\mathbf{\begin{aligned}d_2 & =a_1^2+4 a_2 \\d_4 & =2 a_4+a_1 a_3 \\d_6 & =a_3^2+4 a_6 \\d_8 & =a_1^2 a_6+4 a_2 a_6-a_1 a_3 a_4+a_2 a_3^2-a_4^2 \\c_4 & =d_2^2-24 d_4 \\\Delta & =-d_2^2 d_8-8 d_4^3-27 d_6^2+9 d_2 d_4 d_6\end{aligned}}$