Invariants
| Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $4 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $6^{4}\cdot24^{2}$ | Cusp orbits | $2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 6$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 4$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24D4 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}23&185\\188&235\end{bmatrix}$, $\begin{bmatrix}29&34\\112&169\end{bmatrix}$, $\begin{bmatrix}91&162\\28&227\end{bmatrix}$, $\begin{bmatrix}103&192\\24&1\end{bmatrix}$, $\begin{bmatrix}211&208\\160&257\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.72.4.mi.1 for the level structure with $-I$) |
| Cyclic 264-isogeny field degree: | $96$ |
| Cyclic 264-torsion field degree: | $3840$ |
| Full 264-torsion field degree: | $6758400$ |
Rational points
This modular curve has no $\Q_p$ points for $p=7$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.72.2-24.cu.1.27 | $24$ | $2$ | $2$ | $2$ | $0$ |
| 132.72.2-132.w.1.7 | $132$ | $2$ | $2$ | $2$ | $?$ |
| 264.48.0-264.dm.1.1 | $264$ | $3$ | $3$ | $0$ | $?$ |
| 264.72.2-132.w.1.21 | $264$ | $2$ | $2$ | $2$ | $?$ |
| 264.72.2-24.cu.1.4 | $264$ | $2$ | $2$ | $2$ | $?$ |
| 264.72.2-264.cv.1.11 | $264$ | $2$ | $2$ | $2$ | $?$ |
| 264.72.2-264.cv.1.26 | $264$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 264.288.7-264.doy.1.7 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.dpa.1.5 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.dpo.1.7 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.dpq.1.5 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.dzs.1.19 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.dzu.1.11 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.eam.1.11 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.eao.1.11 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.ejw.1.3 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.ejy.1.6 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.ekm.1.3 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.eko.1.6 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.ets.1.10 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.etu.1.10 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.eui.1.10 | $264$ | $2$ | $2$ | $7$ |
| 264.288.7-264.euk.1.10 | $264$ | $2$ | $2$ | $7$ |