Invariants
Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $2^{8}\cdot6^{8}\cdot8^{4}\cdot24^{4}$ | Cusp orbits | $2^{8}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24Z5 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}7&120\\120&89\end{bmatrix}$, $\begin{bmatrix}37&192\\188&73\end{bmatrix}$, $\begin{bmatrix}103&204\\70&155\end{bmatrix}$, $\begin{bmatrix}205&0\\236&91\end{bmatrix}$, $\begin{bmatrix}229&120\\24&55\end{bmatrix}$, $\begin{bmatrix}259&204\\256&65\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.192.5.mo.4 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $24$ |
Cyclic 264-torsion field degree: | $1920$ |
Full 264-torsion field degree: | $2534400$ |
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 |
---|---|---|---|---|---|
12.192.1-12.b.3.2 | $12$ | $2$ | $2$ | $1$ | $0$ |
264.192.1-12.b.3.8 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.sm.1.10 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.sm.1.23 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.sx.1.10 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.sx.1.23 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.3-264.ds.2.11 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.ds.2.31 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.ff.1.38 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.ff.1.55 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.pv.2.14 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.pv.2.19 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.qg.2.14 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.qg.2.19 | $264$ | $2$ | $2$ | $3$ | $?$ |