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: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | 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: | 8K1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}13&84\\108&143\end{bmatrix}$, $\begin{bmatrix}29&40\\72&113\end{bmatrix}$, $\begin{bmatrix}73&96\\92&113\end{bmatrix}$, $\begin{bmatrix}89&4\\104&143\end{bmatrix}$, $\begin{bmatrix}157&52\\64&131\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.96.1.bu.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $32$ |
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 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 |
---|---|---|---|---|---|---|
8.96.1-8.h.1.2 | $8$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
168.96.0-168.b.2.17 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.b.2.42 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.c.1.17 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.c.1.26 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.cx.1.3 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.cx.1.30 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.cy.1.7 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.cy.1.22 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.1-8.h.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.q.2.18 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.q.2.29 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.s.2.15 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.s.2.18 | $168$ | $2$ | $2$ | $1$ | $?$ | 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.ej.2.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ej.3.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ek.2.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ek.3.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ep.2.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ep.3.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.eq.2.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.eq.4.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |