Invariants
Level: | $168$ | $\SL_2$-level: | $24$ | 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: | $\begin{bmatrix}59&156\\151&97\end{bmatrix}$, $\begin{bmatrix}91&48\\39&137\end{bmatrix}$, $\begin{bmatrix}97&84\\53&55\end{bmatrix}$, $\begin{bmatrix}101&96\\31&115\end{bmatrix}$, $\begin{bmatrix}125&144\\117&67\end{bmatrix}$, $\begin{bmatrix}127&36\\87&85\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 84.96.1.i.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $16$ |
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 |
---|---|---|---|---|---|---|
24.96.1-12.h.1.23 | $24$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
168.96.0-84.c.1.17 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-84.c.1.48 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-84.c.2.5 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-84.c.2.36 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.1-12.h.1.17 | $168$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
168.384.5-84.z.1.18 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-84.ba.2.21 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-84.bd.1.16 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-84.be.1.23 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ry.1.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.rz.2.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.se.1.11 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.sf.1.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.sm.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.sn.2.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.sy.1.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.sz.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ti.1.32 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.tl.2.32 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.tu.1.31 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.tx.2.30 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.tz.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ug.1.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ul.1.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.us.1.14 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ux.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.va.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.vd.1.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.vg.1.16 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.9-168.bdf.2.22 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
168.384.9-168.bdh.2.14 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
168.384.9-168.bdr.2.22 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
168.384.9-168.bdt.2.14 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
168.384.9-168.bfa.2.14 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
168.384.9-168.bff.2.22 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
168.384.9-168.bfm.2.14 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |
168.384.9-168.bfr.2.22 | $168$ | $2$ | $2$ | $9$ | $?$ | not computed |