@misc{specialvalues2025,
  author       = {Koustav Mondal},
  title        = {The Special Values Database},
  howpublished = {\url{https://koustav1997.github.io/Special-Values-Database/}},
  year         = {2025},
  note         = {[Online; accessed ]}
}

Special Values Database

Introduction

This database collects special values of modular functions at CM points, with particular emphasis on the Dedekind eta function \( \eta(\tau) \) and the modular \( j \)-invariant.

The Dedekind eta function is defined by \[ \eta(\tau) = q^{1/24} \prod_{n=1}^{\infty} (1 - q^n), \quad q = e^{2\pi i\tau}, \] and transforms as a modular form of weight \( \tfrac{1}{2} \).

The modular invariant \( j(\tau) \) classifies elliptic curves over \( \mathbb{C} \) up to isomorphism. For CM points \( \tau \), the value \( j(\tau) \) is an algebraic integer generating the Hilbert class field of the corresponding imaginary quadratic order.

CM Discriminants