Invariants
Level: | $168$ | $\SL_2$-level: | $8$ | 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: | $16$ (of which $4$ are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}55&104\\112&153\end{bmatrix}$, $\begin{bmatrix}81&112\\136&41\end{bmatrix}$, $\begin{bmatrix}83&60\\108&143\end{bmatrix}$, $\begin{bmatrix}99&16\\136&33\end{bmatrix}$, $\begin{bmatrix}123&92\\8&97\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.96.1.cz.2 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $64$ |
Cyclic 168-torsion field degree: | $1536$ |
Full 168-torsion field degree: | $774144$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.96.0-8.c.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.96.0-168.b.1.14 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.b.1.39 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-8.c.1.4 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.1-168.o.2.33 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.o.2.48 | $168$ | $2$ | $2$ | $1$ | $?$ | 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.hf.1.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hf.1.14 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hg.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hg.1.11 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hi.2.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hi.2.13 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hj.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hj.1.11 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hm.1.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hm.1.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hn.2.2 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hn.2.16 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hr.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hr.1.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hv.4.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hv.4.15 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |