Affine models of the modular curves \(X(p)\) and its application (Q631502)

For a prime \(p\geq 7\) the authors construct an affine model \(\Phi_p(X,Y)=0\) of the modular curve \(X(p)\) and generate the ray class field modulo \(p\) of the imaginary quadratic field \(K\) as \(K_{(p)}=K(f_1(\theta),f_2(\theta))\), where \(f_1,f_2\) are certain functions satisfying \(\Phi_p(f_1,f_2)=0\) and the ring of integers of \(K\) is \({\mathbb Z}[\theta]\).