Invariants
Level: | $168$ | $\SL_2$-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
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}23&87\\128&13\end{bmatrix}$, $\begin{bmatrix}23&114\\164&151\end{bmatrix}$, $\begin{bmatrix}47&114\\48&41\end{bmatrix}$, $\begin{bmatrix}113&66\\48&5\end{bmatrix}$, $\begin{bmatrix}135&19\\64&33\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.96.3.me.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $16$ |
Cyclic 168-torsion field degree: | $384$ |
Full 168-torsion field degree: | $774144$ |
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 |
---|---|---|---|---|---|
24.96.1-24.iu.1.18 | $24$ | $2$ | $2$ | $1$ | $0$ |
84.96.1-84.k.1.5 | $84$ | $2$ | $2$ | $1$ | $?$ |
168.48.0-168.co.1.13 | $168$ | $4$ | $4$ | $0$ | $?$ |
168.96.1-84.k.1.22 | $168$ | $2$ | $2$ | $1$ | $?$ |
168.96.1-24.iu.1.7 | $168$ | $2$ | $2$ | $1$ | $?$ |
168.96.1-168.zv.1.21 | $168$ | $2$ | $2$ | $1$ | $?$ |
168.96.1-168.zv.1.36 | $168$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
168.384.5-168.bah.1.9 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bah.2.9 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bah.3.3 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bah.4.5 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bal.1.9 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bal.2.9 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bal.3.3 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bal.4.5 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bhb.1.9 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bhb.2.9 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bhb.3.5 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bhb.4.9 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bhf.1.9 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bhf.2.9 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bhf.3.5 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bhf.4.9 | $168$ | $2$ | $2$ | $5$ |