Invariants
Level: | $168$ | $\SL_2$-level: | $12$ | 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 | $2^{6}\cdot4$ | ||
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: | $\begin{bmatrix}1&66\\114&23\end{bmatrix}$, $\begin{bmatrix}11&54\\48&115\end{bmatrix}$, $\begin{bmatrix}61&162\\36&163\end{bmatrix}$, $\begin{bmatrix}85&78\\82&17\end{bmatrix}$, $\begin{bmatrix}167&78\\70&65\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.96.1.lp.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $32$ |
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 |
---|---|---|---|---|---|---|
12.96.0-12.a.2.9 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.96.0-12.a.2.11 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.o.1.28 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.o.1.29 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.1-168.dh.1.8 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.dh.1.13 | $168$ | $2$ | $2$ | $1$ | $?$ | 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.is.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.iw.4.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ix.1.23 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.jc.4.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.kc.2.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ki.3.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.kq.1.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.kw.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.og.2.11 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.oh.2.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ol.1.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.on.4.11 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.pr.1.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ps.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.qf.2.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.qg.3.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |