Invariants
| Level: | $264$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $4$ are rational) | Cusp widths | $4^{6}\cdot12^{6}$ | Cusp orbits | $1^{4}\cdot2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12L3 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}73&114\\240&109\end{bmatrix}$, $\begin{bmatrix}93&20\\16&263\end{bmatrix}$, $\begin{bmatrix}101&228\\8&79\end{bmatrix}$, $\begin{bmatrix}109&32\\216&83\end{bmatrix}$, $\begin{bmatrix}111&50\\184&209\end{bmatrix}$, $\begin{bmatrix}119&34\\260&135\end{bmatrix}$, $\begin{bmatrix}255&38\\100&125\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.96.3.ed.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $24$ |
| Cyclic 264-torsion field degree: | $1920$ |
| Full 264-torsion field degree: | $5068800$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.96.1-12.b.1.12 | $12$ | $2$ | $2$ | $1$ | $0$ |
| 264.96.0-264.o.1.6 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.96.0-264.o.1.23 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.96.1-12.b.1.13 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.96.2-264.b.1.10 | $264$ | $2$ | $2$ | $2$ | $?$ |
| 264.96.2-264.b.1.23 | $264$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.