Invariants
Level: | $264$ | $\SL_2$-level: | $66$ | Newform level: | $1$ | ||
Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $13 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{2}\cdot6^{2}\cdot22^{2}\cdot66^{2}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 24$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 13$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 66A13 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}81&31\\5&88\end{bmatrix}$, $\begin{bmatrix}116&195\\17&70\end{bmatrix}$, $\begin{bmatrix}136&249\\169&23\end{bmatrix}$, $\begin{bmatrix}229&213\\43&158\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.192.13.cq.3 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $12$ |
Cyclic 264-torsion field degree: | $960$ |
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 |
---|---|---|---|---|---|
132.192.7-132.b.1.6 | $132$ | $2$ | $2$ | $7$ | $?$ |
264.192.5-264.qy.3.9 | $264$ | $2$ | $2$ | $5$ | $?$ |
264.192.5-264.qy.3.18 | $264$ | $2$ | $2$ | $5$ | $?$ |
264.192.7-132.b.1.16 | $264$ | $2$ | $2$ | $7$ | $?$ |
264.192.7-264.k.3.3 | $264$ | $2$ | $2$ | $7$ | $?$ |
264.192.7-264.k.3.25 | $264$ | $2$ | $2$ | $7$ | $?$ |