Invariants
Level: | $168$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $3^{8}\cdot12^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12S1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}17&96\\42&95\end{bmatrix}$, $\begin{bmatrix}59&76\\57&127\end{bmatrix}$, $\begin{bmatrix}131&10\\24&61\end{bmatrix}$, $\begin{bmatrix}149&108\\75&119\end{bmatrix}$, $\begin{bmatrix}161&88\\45&115\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.72.1.br.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $32$ |
Cyclic 168-torsion field degree: | $1536$ |
Full 168-torsion field degree: | $1032192$ |
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 |
---|---|---|---|---|---|---|
24.72.0-6.a.1.4 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
42.72.0-6.a.1.1 | $42$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.48.0-168.fj.1.4 | $168$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
168.48.0-168.fj.1.30 | $168$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
168.288.5-168.d.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.ea.1.2 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.iq.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.iu.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bdv.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bdy.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.beq.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bet.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bil.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bin.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bke.1.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bkm.1.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.boi.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bom.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bpr.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bpv.1.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |