\(q\)-expansion of \(j\)-invariant#

sage.modular.modform.j_invariant.j_invariant_qexp(prec=10, K=Rational Field)[source]#

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

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)

Python

>>> from sage.all import *
>>> j_invariant_qexp(Integer(4))
q^-1 + 744 + 196884*q + 21493760*q^2 + 864299970*q^3 + O(q^4)
>>> j_invariant_qexp(Integer(2))
q^-1 + 744 + 196884*q + O(q^2)
>>> j_invariant_qexp(Integer(100), GF(Integer(2)))
q^-1 + q^7 + q^15 + q^31 + q^47 + q^55 + q^71 + q^87 + O(q^100)