Invariants
Level: | $168$ | $\SL_2$-level: | $6$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $6^{4}$ | Cusp orbits | $1^{2}\cdot2$ | ||
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: | 6D1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}5&3\\51&104\end{bmatrix}$, $\begin{bmatrix}33&20\\140&87\end{bmatrix}$, $\begin{bmatrix}73&141\\33&64\end{bmatrix}$, $\begin{bmatrix}139&102\\147&19\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 84.24.1.g.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $96$ |
Cyclic 168-torsion field degree: | $4608$ |
Full 168-torsion field degree: | $3096576$ |
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 |
---|---|---|---|---|---|---|
24.24.0-3.a.1.4 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.16.0-84.b.1.2 | $168$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
168.16.0-84.b.1.8 | $168$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
168.24.0-3.a.1.2 | $168$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
168.144.1-84.u.1.2 | $168$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
168.192.5-84.bt.1.2 | $168$ | $4$ | $4$ | $5$ | $?$ | not computed |
168.384.13-84.k.1.2 | $168$ | $8$ | $8$ | $13$ | $?$ | not computed |