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: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12P1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}25&134\\0&101\end{bmatrix}$, $\begin{bmatrix}67&14\\148&45\end{bmatrix}$, $\begin{bmatrix}83&130\\110&93\end{bmatrix}$, $\begin{bmatrix}139&62\\106&159\end{bmatrix}$, $\begin{bmatrix}157&102\\126&55\end{bmatrix}$, $\begin{bmatrix}165&58\\148&117\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.48.1.dh.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 is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
12.48.0-6.a.1.9 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.48.0-6.a.1.1 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.0-168.fj.1.13 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.0-168.fj.1.20 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.1-168.hm.1.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.48.1-168.hm.1.28 | $168$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
168.192.1-168.lp.1.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.lp.2.6 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.lp.3.12 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.lp.4.16 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.lr.1.6 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.lr.2.8 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.lr.3.10 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.lr.4.12 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.3-168.cs.1.18 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.ct.1.8 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.cu.1.3 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.cv.1.10 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.dh.1.30 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.dj.1.30 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.dn.1.32 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.dp.1.32 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.ep.1.6 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.ep.2.16 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.er.1.4 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.er.2.10 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.fk.1.2 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.fk.2.12 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.fl.1.8 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.fl.2.14 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.288.5-168.d.1.10 | $168$ | $3$ | $3$ | $5$ | $?$ | not computed |