acb_modular_j
Synopsis
#include <flint/acb_modular.h>Sets z to Klein's j-invariant, normalised so that j(i) = 1728, computed on the fundamental domain as j(\tau) = 32 (\theta_2^8+\theta_3^8+\theta_4^8)^3 / (\theta_2 \theta_3 \theta_4)^8 with \theta_i = \theta_i(0, \tau). The output is indeterminate unless \operatorname{Im}(\tau) is certainly positive.
Cite this page
The FLINT team, “acb_modular_j (acb_modular.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_modular/acb_modular_j.html (generated 2026-10-20).
@misc{flint-doc-acb-modular-acb-modular-j,
author = {{The FLINT team}},
title = {{acb\_modular\_j (acb\_modular.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_modular/acb_modular_j.html},
note = {Generated 2026-10-20}
}