Invariants
Level: | $168$ | $\SL_2$-level: | $8$ | Newform level: | $1568$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{6}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}1&0\\20&95\end{bmatrix}$, $\begin{bmatrix}7&16\\40&69\end{bmatrix}$, $\begin{bmatrix}25&132\\144&19\end{bmatrix}$, $\begin{bmatrix}127&100\\36&7\end{bmatrix}$, $\begin{bmatrix}145&56\\8&131\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 56.96.1.x.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $64$ |
Cyclic 168-torsion field degree: | $1536$ |
Full 168-torsion field degree: | $774144$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | 1568.2.a.e |
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 |
---|---|---|---|---|---|---|
24.96.0-8.c.1.3 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.96.0-56.b.2.11 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-56.b.2.18 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-8.c.1.4 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.1-56.o.2.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-56.o.2.18 | $168$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
168.384.5-56.x.1.2 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.x.1.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.y.2.2 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.y.2.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.ba.2.2 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.ba.2.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.bb.3.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.bb.3.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hi.2.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hi.2.13 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hk.2.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hk.2.15 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hs.2.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hs.2.16 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hu.1.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hu.1.15 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |