2018-08-13 05:15:54 -0500 received badge ● Student (source) 2018-08-10 05:11:02 -0500 asked a question generating the ring for schoof's division polynomials hello, i want to generate the ring $F_p[x,y]/(y^2-x^3-ax-b)$, which is necessary to compute the division polynomials in schoof's algorithm to compute the amount of elements of a elliptic curve of the form $y^2=x^3+ax+b$ over $F_p$. I already tried this: R.=PolynomialRing(Zmod(p)) F=R.quo(y^2-x^3-ax-b) x,y=F.gens()  When i computed some division polynomials in the generated F and matched them with division polynomials which sage computed by this: F=Zmod(p) E=EllipticCurve(F,[a,b]) E.division_polynomial()  i saw that my computed division polynomials must be wrong. Does anyone have an idea for generating the Ring $F_p[x,y]/(y^2-x^3-ax-b)$ or generating a "pseudo" elliptic curve in sage, because this code F=Zmod(p) E=EllipticCurve(F,[a,b]) E.division_polynomial()  doesn't work if $p$ isn't prime of course.