sageelliptic-curve

Calculate the y coordinate of a point of a elliptic curve with SAGE?

I defined with SAGE:

p=(10^34+1000).next_prime()
E=EllipticCurve(GF(p),[0,57])

My problem is:

I know the x coordinate of a P of the Elliptic Curve 1407284663933896236729058440000

How can I calculate the y coordinate with SAGE?. Any function?

E([1407284663933896236729058440000, ??????])
Solution 
  • sage: E.lift_x(1407284663933896236729058440000)

(1407284663933896236729058440000 : 4215171991512676773155222850458328 : 1)

    I suggest that you read the Sage reference manual before asking more such questions here.