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: | $\begin{bmatrix}23&250\\96&235\end{bmatrix}$, $\begin{bmatrix}37&42\\96&43\end{bmatrix}$, $\begin{bmatrix}49&32\\214&195\end{bmatrix}$, $\begin{bmatrix}221&162\\18&113\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.192.5.kj.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.d.1.8 | $12$ | $2$ | $2$ | $1$ | $0$ |
264.192.1-12.d.1.1 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.lm.3.9 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.lm.3.32 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.lv.1.14 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.1-264.lv.1.31 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.192.3-264.dk.1.8 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.dk.1.14 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.ej.2.6 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.ej.2.22 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.em.1.24 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.em.1.29 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.ev.2.1 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.192.3-264.ev.2.28 | $264$ | $2$ | $2$ | $3$ | $?$ |