Invariants
Level: | $168$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $1^{4}\cdot2^{2}\cdot3^{4}\cdot6^{2}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24J1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}10&37\\89&66\end{bmatrix}$, $\begin{bmatrix}59&132\\160&43\end{bmatrix}$, $\begin{bmatrix}101&152\\138&43\end{bmatrix}$, $\begin{bmatrix}124&73\\59&42\end{bmatrix}$, $\begin{bmatrix}154&1\\65&126\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.96.1.tb.2 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $16$ |
Cyclic 168-torsion field degree: | $384$ |
Full 168-torsion field degree: | $774144$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
24.96.1-24.iu.1.18 | $24$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
84.96.0-84.c.1.5 | $84$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-84.c.1.3 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.dp.1.48 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.dp.1.50 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.1-24.iu.1.12 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
168.384.5-168.qp.2.21 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.rm.4.16 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ux.1.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.vc.4.16 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.vl.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.vp.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.yt.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.za.1.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bhb.4.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bhh.4.14 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bhr.2.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bhx.4.14 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bjn.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bjt.1.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bkd.2.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bkj.2.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |