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 | $4^{8}\cdot8^{2}$ | Cusp orbits | $2^{5}$ | ||
| 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: | 8N0 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}63&142\\164&257\end{bmatrix}$, $\begin{bmatrix}113&124\\140&237\end{bmatrix}$, $\begin{bmatrix}119&86\\56&87\end{bmatrix}$, $\begin{bmatrix}215&210\\64&259\end{bmatrix}$, $\begin{bmatrix}233&96\\220&179\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.48.0.bc.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 |
|---|---|---|---|---|---|
| 8.48.0-8.e.2.13 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 132.48.0-132.c.1.4 | $132$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-132.c.1.19 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-8.e.2.4 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-264.t.1.3 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-264.t.1.60 | $264$ | $2$ | $2$ | $0$ | $?$ |
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.be.2.9 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.da.2.10 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.dy.2.12 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.eg.2.7 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.iz.2.14 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.jh.2.10 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.jo.2.6 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.jw.2.14 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.mu.2.10 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.nc.2.14 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.nl.2.11 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.nt.2.9 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.pg.2.12 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.po.2.13 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.pt.2.13 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.px.2.12 | $264$ | $2$ | $2$ | $1$ |
| 264.288.8-264.df.1.37 | $264$ | $3$ | $3$ | $8$ |
| 264.384.7-264.dd.1.61 | $264$ | $4$ | $4$ | $7$ |