Invariants
| Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{2}\cdot8^{2}\cdot12^{2}\cdot24^{2}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24I5 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}1&63\\166&227\end{bmatrix}$, $\begin{bmatrix}65&19\\234&211\end{bmatrix}$, $\begin{bmatrix}77&216\\78&239\end{bmatrix}$, $\begin{bmatrix}119&136\\164&111\end{bmatrix}$, $\begin{bmatrix}171&263\\50&93\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.96.5.ir.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $48$ |
| Cyclic 264-torsion field degree: | $3840$ |
| Full 264-torsion field degree: | $5068800$ |
Rational points
This modular curve has no $\Q_p$ points for $p=17,29$, and therefore no 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.o.1.3 | $12$ | $2$ | $2$ | $1$ | $0$ |
| 264.96.1-12.o.1.13 | $264$ | $2$ | $2$ | $1$ | $?$ |
| 264.96.3-264.ce.1.45 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.96.3-264.ce.1.60 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.96.3-264.cn.1.45 | $264$ | $2$ | $2$ | $3$ | $?$ |
| 264.96.3-264.cn.1.60 | $264$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 264.384.9-264.cgx.1.9 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cgy.1.9 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cgz.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cha.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cid.1.1 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cie.1.1 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cif.1.14 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cig.1.14 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cit.1.2 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.ciu.1.2 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.civ.1.13 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.ciw.1.13 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cjj.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cjk.1.10 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cjl.1.9 | $264$ | $2$ | $2$ | $9$ |
| 264.384.9-264.cjm.1.9 | $264$ | $2$ | $2$ | $9$ |