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: | $\begin{bmatrix}5&108\\36&71\end{bmatrix}$, $\begin{bmatrix}71&118\\114&115\end{bmatrix}$, $\begin{bmatrix}107&76\\138&73\end{bmatrix}$, $\begin{bmatrix}127&62\\108&89\end{bmatrix}$, $\begin{bmatrix}137&6\\63&101\end{bmatrix}$ |
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 |
---|---|---|---|---|---|---|
12.72.0-6.a.1.5 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.48.0-168.fj.1.13 | $168$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
168.48.0-168.fj.1.19 | $168$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
168.72.0-6.a.1.6 | $168$ | $2$ | $2$ | $0$ | $?$ | 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.1.10 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.ea.1.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.iq.1.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.iu.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bdv.1.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bdy.1.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.beq.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bet.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bil.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bin.1.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bke.1.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bkm.1.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.boi.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bom.1.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bpr.1.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bpv.1.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |