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 | $2^{5}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-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: | $\begin{bmatrix}85&224\\88&25\end{bmatrix}$, $\begin{bmatrix}97&208\\66&163\end{bmatrix}$, $\begin{bmatrix}165&208\\104&35\end{bmatrix}$, $\begin{bmatrix}217&40\\164&123\end{bmatrix}$, $\begin{bmatrix}221&184\\26&245\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 264.48.0.cw.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 no real points, and therefore no 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.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 264.48.0-8.i.1.3 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-264.t.1.5 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-264.t.1.25 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-264.ec.2.4 | $264$ | $2$ | $2$ | $0$ | $?$ |
| 264.48.0-264.ec.2.29 | $264$ | $2$ | $2$ | $0$ | $?$ |
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.v.1.2 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.fo.1.3 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.kx.1.2 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.lb.1.2 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.ot.2.3 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.ox.2.5 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.pt.2.3 | $264$ | $2$ | $2$ | $1$ |
| 264.192.1-264.qb.2.3 | $264$ | $2$ | $2$ | $1$ |
| 264.288.8-264.pc.2.41 | $264$ | $3$ | $3$ | $8$ |
| 264.384.7-264.jo.2.1 | $264$ | $4$ | $4$ | $7$ |