Invariants
| Level: | $264$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{2}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8K1 |
Level structure
| $\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}5&124\\182&75\end{bmatrix}$, $\begin{bmatrix}103&116\\48&49\end{bmatrix}$, $\begin{bmatrix}125&88\\26&119\end{bmatrix}$, $\begin{bmatrix}143&192\\106&107\end{bmatrix}$, $\begin{bmatrix}181&0\\140&59\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 264.192.1-264.og.2.1, 264.192.1-264.og.2.2, 264.192.1-264.og.2.3, 264.192.1-264.og.2.4, 264.192.1-264.og.2.5, 264.192.1-264.og.2.6, 264.192.1-264.og.2.7, 264.192.1-264.og.2.8, 264.192.1-264.og.2.9, 264.192.1-264.og.2.10, 264.192.1-264.og.2.11, 264.192.1-264.og.2.12, 264.192.1-264.og.2.13, 264.192.1-264.og.2.14, 264.192.1-264.og.2.15, 264.192.1-264.og.2.16 |
| Cyclic 264-isogeny field degree: | $96$ |
| Cyclic 264-torsion field degree: | $3840$ |
| Full 264-torsion field degree: | $10137600$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
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 | Kernel decomposition |
|---|---|---|---|---|---|---|
| 24.48.0.w.2 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 88.48.1.bi.1 | $88$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.48.0.bj.2 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 264.48.0.bm.1 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 264.48.0.cq.1 | $264$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 264.48.1.dr.2 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 264.48.1.fe.1 | $264$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 264.288.17.jbo.1 | $264$ | $3$ | $3$ | $17$ | $?$ | not computed |
| 264.384.17.dqg.2 | $264$ | $4$ | $4$ | $17$ | $?$ | not computed |