ellformalw

Function: ellformalw
Section: elliptic_curves
C-Name: ellformalw
Prototype: GDPDn
Help:ellformalw(E, {n = seriesprecision}, {t = 'x}): E elliptic curve,
 n integer; returns n terms of the formal expansion of w = -1/y in the formal
 parameter t = -x/y.
Doc:Return the formal power series $w$ attached to the elliptic curve $E$,
 in the variable $t$:
 $$ w(t) = t^3(1 + a_1 t + (a_2 + a_1^2) t^2 + \cdots + O(t^{n})),$$
 which is the formal expansion of $-1/y$ in the formal parameter $t := -x/y$
 at $\infty$ (take $n = \tet{seriesprecision}$ if $n$ is omitted). The
 coefficients of $w$ belong to $\Z[a_1,a_2,a_3,a_4,a_6]$.
 \bprog
 ? E=ellinit([3,2,-4,-2,5]); ellformalw(E, 5, 't)
 %1 = t^3 + 3*t^4 + 11*t^5 + 35*t^6 + 101*t^7 + O(t^8)
 @eprog