Invariants
Level: | $264$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-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 | $8^{24}$ | Cusp orbits | $2^{2}\cdot4^{3}\cdot8$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8A5 |
Level structure
$\GL_2(\Z/264\Z)$-generators: | $\begin{bmatrix}63&110\\92&133\end{bmatrix}$, $\begin{bmatrix}129&56\\28&145\end{bmatrix}$, $\begin{bmatrix}147&92\\92&155\end{bmatrix}$, $\begin{bmatrix}149&52\\8&101\end{bmatrix}$, $\begin{bmatrix}203&64\\92&263\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 264.384.5-264.fb.2.1, 264.384.5-264.fb.2.2, 264.384.5-264.fb.2.3, 264.384.5-264.fb.2.4, 264.384.5-264.fb.2.5, 264.384.5-264.fb.2.6, 264.384.5-264.fb.2.7, 264.384.5-264.fb.2.8, 264.384.5-264.fb.2.9, 264.384.5-264.fb.2.10, 264.384.5-264.fb.2.11, 264.384.5-264.fb.2.12, 264.384.5-264.fb.2.13, 264.384.5-264.fb.2.14, 264.384.5-264.fb.2.15, 264.384.5-264.fb.2.16 |
Cyclic 264-isogeny field degree: | $96$ |
Cyclic 264-torsion field degree: | $7680$ |
Full 264-torsion field degree: | $5068800$ |
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 |
---|---|---|---|---|---|
24.96.1.n.2 | $24$ | $2$ | $2$ | $1$ | $1$ |
88.96.3.q.2 | $88$ | $2$ | $2$ | $3$ | $?$ |
264.96.1.bx.2 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.1.bz.1 | $264$ | $2$ | $2$ | $1$ | $?$ |
264.96.3.bm.3 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.96.3.bs.1 | $264$ | $2$ | $2$ | $3$ | $?$ |
264.96.3.cc.1 | $264$ | $2$ | $2$ | $3$ | $?$ |