Invariants
Level: | $168$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12P1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}31&147\\94&59\end{bmatrix}$, $\begin{bmatrix}49&8\\60&89\end{bmatrix}$, $\begin{bmatrix}149&139\\50&63\end{bmatrix}$, $\begin{bmatrix}157&99\\58&161\end{bmatrix}$, $\begin{bmatrix}159&85\\62&115\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.48.1.bzu.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $32$ |
Cyclic 168-torsion field degree: | $1536$ |
Full 168-torsion field degree: | $1548288$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
12.48.1-12.k.1.2 | $12$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
168.48.0-168.fk.1.20 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.0-168.fk.1.21 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.0-168.fn.1.10 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.0-168.fn.1.27 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.1-12.k.1.8 | $168$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
168.192.5-168.db.1.13 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.192.5-168.dd.1.19 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.192.5-168.nm.1.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.192.5-168.np.1.11 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.192.5-168.tq.1.11 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.192.5-168.tt.1.13 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.192.5-168.ux.1.19 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.192.5-168.uz.1.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bzn.1.4 | $168$ | $3$ | $3$ | $5$ | $?$ | not computed |