# 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 $$K$$.

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)