Invariants
Level: | $264$ | $\SL_2$-level: | $12$ | 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 | $4^{12}\cdot12^{12}$ | Cusp orbits | $2^{4}\cdot4^{4}$ | ||
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: | 12E5 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}33&202\\182&121\end{bmatrix}$, $\begin{bmatrix}61&216\\252&91\end{bmatrix}$, $\begin{bmatrix}145&120\\252&235\end{bmatrix}$, $\begin{bmatrix}167&208\\60&55\end{bmatrix}$, $\begin{bmatrix}263&78\\74&241\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.192.5.in.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $48$ |
Cyclic 264-torsion field degree: | $1920$ |
Full 264-torsion field degree: | $2534400$ |
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 |
---|---|---|---|---|---|
12.192.1-12.a.2.6 | $12$ | $2$ | $2$ | $1$ | $0$ |
264.192.1-12.a.2.1 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.lm.1.13 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.lm.1.27 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.lm.3.9 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.lm.3.23 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.3-264.cq.1.5 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.cq.1.16 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.ea.2.8 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.ea.2.28 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.em.2.5 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.em.2.8 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.em.2.10 | $264$ | $2$ | $2$ | $3$ | $?$ |