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: | $\begin{bmatrix}23&260\\194&97\end{bmatrix}$, $\begin{bmatrix}117&148\\88&39\end{bmatrix}$, $\begin{bmatrix}147&236\\22&259\end{bmatrix}$, $\begin{bmatrix}189&184\\112&77\end{bmatrix}$, $\begin{bmatrix}257&132\\56&191\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.48.0.bq.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $96$ |
| Cyclic 264-torsion field degree: | $7680$ |
| 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.h.1.32 | $24$ | $2$ | $2$ | $0$ | $0$ |
| 88.48.0-88.i.1.24 | $88$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-24.h.1.20 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-88.i.1.20 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-264.x.1.35 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-264.x.1.38 | $264$ | $2$ | $2$ | $0$ | $?$ |
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.g.1.15 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.k.1.13 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.ck.2.3 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.co.1.15 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.du.2.12 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.dv.2.6 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.ec.1.12 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.ed.1.15 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.gi.2.4 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.gj.1.14 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.gq.1.16 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.gr.1.13 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.gy.1.11 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.gz.1.15 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.hg.2.11 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.hh.1.11 | $264$ | $2$ | $2$ | $1$ |
| 264.288.8-264.ls.2.63 | $264$ | $3$ | $3$ | $8$ |
| 264.384.7-264.gl.1.58 | $264$ | $4$ | $4$ | $7$ |