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 | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | 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: | 12V1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}11&48\\142&127\end{bmatrix}$, $\begin{bmatrix}19&72\\149&157\end{bmatrix}$, $\begin{bmatrix}25&72\\51&131\end{bmatrix}$, $\begin{bmatrix}29&0\\139&55\end{bmatrix}$, $\begin{bmatrix}79&12\\58&71\end{bmatrix}$, $\begin{bmatrix}101&108\\119&47\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.96.1.qt.2 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $16$ |
Cyclic 168-torsion field degree: | $768$ |
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 |
---|---|---|---|---|---|---|
24.96.1-12.h.1.23 | $24$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
168.96.0-168.dq.1.20 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.dq.1.63 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.dq.2.4 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.dq.2.55 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.1-12.h.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.rx.2.2 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.sa.2.11 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.sd.1.12 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.sg.2.14 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.sj.2.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.sq.2.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.sv.1.10 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.tc.2.10 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.th.2.22 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.tj.2.28 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.tk.1.23 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.tm.1.31 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.tt.2.19 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.tv.2.23 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.tw.1.21 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ty.1.29 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.uc.2.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ud.2.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.uo.2.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.up.2.11 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.uy.2.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.uz.2.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ve.2.13 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.vf.2.15 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.9-168.bdd.1.10 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
168.384.9-168.bdk.1.10 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
168.384.9-168.bdp.1.11 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
168.384.9-168.bdw.1.11 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
168.384.9-168.bey.1.11 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
168.384.9-168.bfh.1.10 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
168.384.9-168.bfk.1.13 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
168.384.9-168.bft.1.11 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |