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: | $\begin{bmatrix}3&112\\104&143\end{bmatrix}$, $\begin{bmatrix}94&127\\17&156\end{bmatrix}$, $\begin{bmatrix}122&147\\13&160\end{bmatrix}$, $\begin{bmatrix}138&1\\73&54\end{bmatrix}$, $\begin{bmatrix}158&15\\115&82\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.96.1.tg.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.ix.1.22 | $24$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
168.96.0-168.dp.1.13 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.dp.1.34 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.dq.2.21 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.dq.2.36 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.1-24.ix.1.16 | $168$ | $2$ | $2$ | $1$ | $?$ | 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.qv.2.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.rs.4.16 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.vf.2.13 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.vi.4.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.xh.4.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.xm.3.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.yv.3.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.za.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bhk.2.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bhq.3.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bia.4.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.big.4.13 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bjw.4.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bkc.3.11 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bkm.3.2 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bks.1.2 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |