Invariants
Level: | $264$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $2^{4}\cdot6^{4}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $2^{6}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24V3 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}31&258\\24&211\end{bmatrix}$, $\begin{bmatrix}49&246\\228&61\end{bmatrix}$, $\begin{bmatrix}53&192\\12&89\end{bmatrix}$, $\begin{bmatrix}73&108\\208&65\end{bmatrix}$, $\begin{bmatrix}199&158\\72&83\end{bmatrix}$, $\begin{bmatrix}225&1\\40&255\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 264.96.3.hk.1 for the level structure with $-I$) |
Cyclic 264-isogeny field degree: | $24$ |
Cyclic 264-torsion field degree: | $1920$ |
Full 264-torsion field degree: | $5068800$ |
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 |
---|---|---|---|---|---|
24.96.1-12.h.1.23 | $24$ | $2$ | $2$ | $1$ | $0$ |
132.96.1-12.h.1.5 | $132$ | $2$ | $2$ | $1$ | $?$ |
264.48.0-264.bf.1.8 | $264$ | $4$ | $4$ | $0$ | $?$ |
264.96.1-264.zu.1.2 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.1-264.zu.1.10 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.1-264.zu.1.55 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.1-264.zu.1.63 | $264$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.