Invariants
Level: | $168$ | $\SL_2$-level: | $8$ | Newform level: | $3136$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (of which $2$ are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot8$ | ||
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: | 8K1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}31&88\\92&135\end{bmatrix}$, $\begin{bmatrix}55&142\\48&157\end{bmatrix}$, $\begin{bmatrix}81&44\\140&53\end{bmatrix}$, $\begin{bmatrix}115&2\\44&81\end{bmatrix}$, $\begin{bmatrix}131&74\\96&161\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 56.96.1.n.2 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $64$ |
Cyclic 168-torsion field degree: | $3072$ |
Full 168-torsion field degree: | $774144$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | 3136.2.a.m |
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.b.1.12 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.96.0-8.b.1.2 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-56.b.1.19 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.0-56.b.1.24 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.96.1-56.n.1.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-56.n.1.12 | $168$ | $2$ | $2$ | $1$ | $?$ | 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.d.2.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.f.3.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.h.2.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.k.3.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.p.2.4 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.s.4.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.z.2.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-56.bb.4.8 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bu.1.12 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.bw.2.11 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.do.2.15 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.dq.1.11 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.eu.1.13 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ew.2.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.ha.2.13 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.384.5-168.hc.1.9 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |