\(q\)-expansion of \(j\)-invariant#
- sage.modular.modform.j_invariant.j_invariant_qexp(prec=10, K=Rational Field)#
Return the \(q\)-expansion of the \(j\)-invariant to precision
prec
in the field \(K\).See also
If you want to evaluate (numerically) the \(j\)-invariant at certain points, see the special function
elliptic_j()
.Warning
Stupid algorithm – we divide by Delta, which is slow.
EXAMPLES:
sage: j_invariant_qexp(4) q^-1 + 744 + 196884*q + 21493760*q^2 + 864299970*q^3 + O(q^4) sage: j_invariant_qexp(2) q^-1 + 744 + 196884*q + O(q^2) sage: j_invariant_qexp(100, GF(2)) q^-1 + q^7 + q^15 + q^31 + q^47 + q^55 + q^71 + q^87 + O(q^100)