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

Question

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, ??????])

score 12 · Accepted Answer · edited Jun 15 '12 at 13:52

12

sage: E.lift_x(1407284663933896236729058440000)

(1407284663933896236729058440000 : 4215171991512676773155222850458328 : 1)

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

edited Jun 15 '12 at 13:52

DSM

answered Jun 15 '12 at 13:27

John Cremona

2

Thank you very much, i read the SAGE manual but i don't find that function. Tahnk you very much and sorry for the inconveniece. – vem Jun 15 '12 at 13:44
3

this response saved me a lot of time so thanks for asking and answering it here :) – David 天宇 Wong Aug 02 '22 at 14:39
2

And here is the [link to the documentation](https://doc.sagemath.org/html/en/reference/arithmetic_curves/sage/schemes/elliptic_curves/ell_generic.html#sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic.lift_x). – Kaspar Etter Aug 15 '22 at 10:00

1 Answers1