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: | $\begin{bmatrix}43&60\\108&109\end{bmatrix}$, $\begin{bmatrix}97&38\\63&167\end{bmatrix}$, $\begin{bmatrix}107&160\\156&163\end{bmatrix}$, $\begin{bmatrix}109&36\\15&97\end{bmatrix}$, $\begin{bmatrix}137&106\\111&79\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 84.72.1.r.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.1.1 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.48.0-84.q.1.5 | $168$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
168.48.0-84.q.1.15 | $168$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
168.72.0-6.a.1.3 | $168$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
168.288.5-84.f.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-84.be.1.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-84.dk.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-84.do.1.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.dt.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-84.fw.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-84.ge.1.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-84.gu.1.2 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-84.gz.1.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.ig.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bbn.1.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bcp.1.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bsq.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.buu.1.2 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bzc.1.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.cal.1.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |