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 | $2^{4}\cdot4^{2}$ | ||
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: | $\begin{bmatrix}7&12\\32&121\end{bmatrix}$, $\begin{bmatrix}55&114\\76&17\end{bmatrix}$, $\begin{bmatrix}79&102\\32&55\end{bmatrix}$, $\begin{bmatrix}91&114\\162&13\end{bmatrix}$, $\begin{bmatrix}133&102\\32&73\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.96.1.lq.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 |
---|---|---|---|---|---|---|
24.96.0-24.o.1.31 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
84.96.1-84.b.1.8 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.0-24.o.1.1 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.o.2.7 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-168.o.2.57 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.1-84.b.1.5 | $168$ | $2$ | $2$ | $1$ | $?$ | 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.it.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.iw.2.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.iy.2.20 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.jd.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.kd.2.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.kh.4.13 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.kr.2.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.kv.3.13 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.oe.2.10 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.oi.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.oj.1.18 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.op.2.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.po.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.pt.3.14 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.qc.1.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.qh.4.14 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |