Invariants
Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $7 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
Cusps: | $20$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{2}\cdot12^{8}\cdot24^{2}$ | Cusp orbits | $2^{6}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 12$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 7$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24AG7 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}75&236\\100&241\end{bmatrix}$, $\begin{bmatrix}81&218\\260&159\end{bmatrix}$, $\begin{bmatrix}175&48\\60&229\end{bmatrix}$, $\begin{bmatrix}195&136\\152&233\end{bmatrix}$, $\begin{bmatrix}199&256\\80&249\end{bmatrix}$, $\begin{bmatrix}207&112\\224&137\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.192.7.y.1 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 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 |
---|---|---|---|---|---|
12.192.3-12.e.1.5 | $12$ | $2$ | $2$ | $3$ | $0$ |
264.96.0-264.j.1.6 | $264$ | $4$ | $4$ | $0$ | $?$ |
264.192.3-12.e.1.17 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.dx.1.19 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.dx.1.48 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.dy.2.83 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.dy.2.112 | $264$ | $2$ | $2$ | $3$ | $?$ |