The **label** of a modular curve $X_H$ is the same as the label of the open subgroup $H\le \GL_2(\widehat\Z)$. When $\det(H)=\widehat\Z^\times$ and $-I\in H$ this label has the form $\texttt{N.i.g.c.n}$, where

- $N$ is the level of $H$
- $i$ is the index of $H$
- $g$ is the genus of $H$
- $c$ is a base-26 ordinal that uniquely identifies the Gassmann class of $H$ among groups of the same level, index, and genus.
- $n$ is a positive integer that distinguishes nonconjugate subgroups of the same level, index, genus, and Gassmann class.

When $\det(H)=\widehat\Z^\times$ and $-I\not \in H$ this label has the form $\texttt{N.i.g-M.c.m.n}$, where $N$, $i$, and $g$ are as above, and

- $N$ is the level of $H$
- $i$ is the index of $H$
- $g$ is the genus of $H$
- $M$ is the level of $H':=\langle H, -I\rangle$
- $c$ is the base-26 ordinal that identifies the Gassmann class of $H'$
- $m$ is the positive integer in the label $\texttt{M.j.g.c.m}$ of $H'$, where $i=2j$.
- $n$ is a positive integer that distinguishes $H$ from nonconjugate refinements of $H'$ of the same level.

**Authors:**

**Knowl status:**

- Review status: beta
- Last edited by Andrew Sutherland on 2023-07-10 07:18:19

**Referred to by:**

- columns.gps_gl2zhat_fine.coarse_class
- columns.gps_gl2zhat_fine.coarse_class_num
- columns.gps_gl2zhat_fine.coarse_label
- columns.gps_gl2zhat_fine.coarse_num
- columns.gps_gl2zhat_fine.factorization
- columns.gps_gl2zhat_fine.label
- columns.gps_gl2zhat_fine.parents
- columns.gps_gl2zhat_test.label
- columns.gps_gl2zhat_test.reductions
- columns.gps_sl2zhat.label
- columns.gps_sl2zhat_temp.label
- columns.modcurve_modelmaps.codomain_label
- columns.modcurve_modelmaps.domain_label
- modcurve.search_input
- lmfdb/elliptic_curves/templates/ec-curve.html (line 479)
- lmfdb/modular_curves/main.py (line 324)
- lmfdb/modular_curves/main.py (line 985)
- lmfdb/modular_curves/main.py (line 1062)
- lmfdb/modular_curves/main.py (line 1243)
- lmfdb/modular_curves/templates/modcurve_isoclass.html (line 18)

**History:**(expand/hide all)

- 2023-07-10 07:18:19 by Andrew Sutherland
- 2023-04-11 13:04:49 by Andrew Sutherland
- 2023-03-18 06:40:35 by Andrew Sutherland
- 2023-01-03 11:22:59 by Andrew Sutherland
- 2022-11-06 15:22:56 by John Voight
- 2022-11-06 15:22:32 by John Voight
- 2022-11-06 15:22:10 by John Voight
- 2022-03-20 21:46:42 by Andrew Sutherland
- 2022-03-20 17:41:04 by Andrew Sutherland
- 2022-03-20 17:36:00 by Andrew Sutherland
- 2022-03-20 17:34:41 by Andrew Sutherland

**Differences**(show/hide)