Consider the elliptic curve $E: x^2 = y^3 + 23x+11$ over p-adic fields. In Sage I use: > k = GF(257) <br> > E = EllipticCurve(k,[23,11]) <br> > kp = Qp(257,5) # 257-adic Field with capped relative precision 5 <br> > Ep = E.change_ring(kp) Now, Ep is the Elliptic Curve defined by y^2 = x^3 + (23+O(257))*x + (11+O(257)) over 257-adic Field with capped relative precision 5. On this curve there is a point with coordinates (1,258). In Sage: > s = Ep([7,258]) <br> > print s <br> > (7 + O(257^5) : 1 + 257 + O(257^5) : 1 + O(257^5)) So far so good, everything works as expected. s has order 83. Therefore 84*s=s. In Sage: > t=84*s <br> > print t <br> > (7 + O(257) : 1 + O(257) : 1 + O(257^5)) Notice how this is indeed the same expression as for s, but evaluated only to lowest order in the p-adic expansion. My question is: How can I evaluate (and display) t to higher orders in the p-adic expansion. Specifically in the example above: How do I recover that the second coordinate of t is 1 + 257 + O(257^5) rather than just 1 + O(257)?