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ID: INPUT{id.yaml}
Title: >
$q$-expansion of the $j$-invariant
Definition: >
This list contains the coefficients of the $j$-invariant CITE{Wiki}
in its $q$-expansion,
$j(\tau) = \sum_{n=-1}^{\infty} a_n q^n$,
where $q = e^{2\pi i\tau}$.
Parameters:
n:
type: Z
constraints: $n \geq -1$
Comments:
Formulas:
Programs:
program-sage:
language: Sage
code: |
numbers = {n: j_invariant_qexp(101)[n] for n in [-1..100]}
References:
Links:
Wiki:
title: "Wikipedia: j-invariant"
url: https://en.wikipedia.org/wiki/J-invariant
WikiMoonshine:
title: "Wikipedia: j-invariant: The q-expansion and moonshine"
url: https://en.wikipedia.org/wiki/J-invariant#The_q-expansion_and_moonshine
Similar tables:
Keywords:
Tags:
- Taylor series
- modular function
- elliptic curves
- number theory
Data properties:
complete: no
Display properties:
number-header: >
$a_n$
Numbers: INPUT{numbers.yaml}
