# points on elliptic curve number field

I have the following elliptic curve : y^2=x^3-3267x+45630 and generator P=[-21,324].

I want to find the general formula to add any point (r,s) to the point ((-15/2)+(27/2)*B,0) where B^2=17.

PARI seems to be pretty straightforward in giving answer. And i think the mistake I did in SAGE is that I should define r and s in number field which I'm not sure how to do it.

The Pari code is as follows :

```
gp > elladd(E,[r,s],[(-15/2)+(27/2)*B,0])= [(-8*r^3 + (108*B - 60)*r^2 + (1458*B^2 - 1620*B + 450)*r + (8*s^2 + (-19683*B^3 + 32805*B^2 - 18225*B + 3375)))/(8*r^2 + (-216*B + 120)*r + (1458*B^2 - 1620*B + 450)), (-8*s*r^3 + (4374*B^2 - 4860*B + 1350)*s*r + (8*s^3 + (-39366*B^3 + 65610*B^2 - 36450*B + 6750)*s))/(-8*r^3 + (324*B - 180)*r^2 + (-4374*B^2 + 4860*B - 1350)*r + (19683*B^3 - 32805*B^2 + 18225*B - 3375))]
```