Invariants
| Level: | $264$ | $\SL_2$-level: | $8$ | ||||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{3}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8O0 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}95&92\\164&85\end{bmatrix}$, $\begin{bmatrix}147&244\\86&103\end{bmatrix}$, $\begin{bmatrix}149&24\\24&121\end{bmatrix}$, $\begin{bmatrix}209&8\\214&125\end{bmatrix}$, $\begin{bmatrix}219&244\\236&225\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.48.0.cl.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $96$ |
| Cyclic 264-torsion field degree: | $3840$ |
| Full 264-torsion field degree: | $10137600$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.48.0-24.l.1.1 | $24$ | $2$ | $2$ | $0$ | $0$ |
| 264.48.0-24.l.1.20 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 88.48.0-88.h.1.11 | $88$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-88.h.1.12 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-264.t.1.8 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-264.t.1.25 | $264$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 264.192.1-264.m.1.3 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.t.2.4 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.w.1.4 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.bh.1.6 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.dc.1.5 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.dd.2.2 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.de.1.7 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.df.1.5 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.mc.2.5 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.md.2.4 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.me.2.7 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.mf.2.11 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.ms.2.9 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.mt.2.2 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.mu.2.13 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.mv.2.9 | $264$ | $2$ | $2$ | $1$ |
| 264.288.8-264.nz.2.33 | $264$ | $3$ | $3$ | $8$ |
| 264.384.7-264.is.2.1 | $264$ | $4$ | $4$ | $7$ |