Invariants
Level: | $168$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $6^{8}\cdot24^{4}$ | Cusp orbits | $2^{4}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 12$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 7$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24J7 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}5&118\\144&61\end{bmatrix}$, $\begin{bmatrix}23&20\\92&69\end{bmatrix}$, $\begin{bmatrix}79&152\\84&53\end{bmatrix}$, $\begin{bmatrix}127&22\\148&125\end{bmatrix}$, $\begin{bmatrix}141&20\\64&57\end{bmatrix}$, $\begin{bmatrix}167&96\\132&41\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.144.7.bjs.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $32$ |
Cyclic 168-torsion field degree: | $1536$ |
Full 168-torsion field degree: | $516096$ |
Rational points
This modular curve has no $\Q_p$ points for $p=19$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.144.4-24.ch.1.38 | $24$ | $2$ | $2$ | $4$ | $0$ |
168.144.3-168.cc.1.23 | $168$ | $2$ | $2$ | $3$ | $?$ |
168.144.3-168.cc.1.46 | $168$ | $2$ | $2$ | $3$ | $?$ |
168.144.3-168.cbb.1.24 | $168$ | $2$ | $2$ | $3$ | $?$ |
168.144.3-168.cbb.1.37 | $168$ | $2$ | $2$ | $3$ | $?$ |
168.144.3-168.ccs.1.12 | $168$ | $2$ | $2$ | $3$ | $?$ |
168.144.3-168.ccs.1.21 | $168$ | $2$ | $2$ | $3$ | $?$ |
168.144.4-168.bh.1.35 | $168$ | $2$ | $2$ | $4$ | $?$ |
168.144.4-168.bh.1.77 | $168$ | $2$ | $2$ | $4$ | $?$ |
168.144.4-24.ch.1.43 | $168$ | $2$ | $2$ | $4$ | $?$ |
168.144.4-168.ob.1.25 | $168$ | $2$ | $2$ | $4$ | $?$ |
168.144.4-168.ob.1.36 | $168$ | $2$ | $2$ | $4$ | $?$ |
168.144.4-168.qe.1.13 | $168$ | $2$ | $2$ | $4$ | $?$ |
168.144.4-168.qe.1.20 | $168$ | $2$ | $2$ | $4$ | $?$ |