Invariants
Level: | $168$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $288$ | ||||
Genus: | $17 = 1 + \frac{ 288 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $12^{8}\cdot24^{8}$ | Cusp orbits | $2^{2}\cdot4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 32$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 17$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24B17 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}3&74\\136&27\end{bmatrix}$, $\begin{bmatrix}25&154\\60&41\end{bmatrix}$, $\begin{bmatrix}37&146\\164&143\end{bmatrix}$, $\begin{bmatrix}73&124\\112&101\end{bmatrix}$, $\begin{bmatrix}85&106\\40&53\end{bmatrix}$, $\begin{bmatrix}115&98\\44&5\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 168-isogeny field degree: | $64$ |
Cyclic 168-torsion field degree: | $1536$ |
Full 168-torsion field degree: | $516096$ |
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 |
---|---|---|---|---|---|
24.144.8.er.1 | $24$ | $2$ | $2$ | $8$ | $0$ |
168.96.1.ns.2 | $168$ | $3$ | $3$ | $1$ | $?$ |
168.144.8.by.1 | $168$ | $2$ | $2$ | $8$ | $?$ |
168.144.8.cd.1 | $168$ | $2$ | $2$ | $8$ | $?$ |
168.144.8.ol.2 | $168$ | $2$ | $2$ | $8$ | $?$ |
168.144.9.sx.1 | $168$ | $2$ | $2$ | $9$ | $?$ |
168.144.9.ta.2 | $168$ | $2$ | $2$ | $9$ | $?$ |
168.144.9.baq.1 | $168$ | $2$ | $2$ | $9$ | $?$ |