Invariants
| Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $2^{2}\cdot6^{2}\cdot8\cdot24$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24F2 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}94&99\\151&188\end{bmatrix}$, $\begin{bmatrix}111&104\\16&125\end{bmatrix}$, $\begin{bmatrix}120&5\\149&210\end{bmatrix}$, $\begin{bmatrix}124&41\\253&138\end{bmatrix}$, $\begin{bmatrix}176&247\\255&142\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.48.2.d.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $48$ |
| Cyclic 264-torsion field degree: | $3840$ |
| Full 264-torsion field degree: | $10137600$ |
Rational points
This modular curve has 2 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 |
|---|---|---|---|---|---|
| 12.48.0-12.f.1.3 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 264.48.0-12.f.1.9 | $264$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 264.192.3-264.dq.1.3 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.fs.2.13 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.gk.2.13 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.gp.2.15 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.jc.2.11 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.je.2.13 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.jg.2.9 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.ji.2.13 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.kj.1.15 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.kk.1.10 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.kn.2.15 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.ko.2.13 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.kz.2.9 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.la.2.7 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.ld.1.13 | $264$ | $2$ | $2$ | $3$ |
| 264.192.3-264.le.1.9 | $264$ | $2$ | $2$ | $3$ |
| 264.288.7-264.czl.1.8 | $264$ | $3$ | $3$ | $7$ |