\(q\)-expansion of \(j\)-invariant - Modular Forms

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# \(q\)-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

      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)