Invariants
Level: | $168$ | $\SL_2$-level: | $8$ | 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: | $4$ (all of which are rational) | Cusp widths | $4^{2}\cdot8^{2}$ | Cusp orbits | $1^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8B1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}11&162\\52&145\end{bmatrix}$, $\begin{bmatrix}19&78\\60&71\end{bmatrix}$, $\begin{bmatrix}55&164\\116&153\end{bmatrix}$, $\begin{bmatrix}91&106\\12&149\end{bmatrix}$, $\begin{bmatrix}91&122\\156&145\end{bmatrix}$, $\begin{bmatrix}159&14\\52&125\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.24.1.d.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $64$ |
Cyclic 168-torsion field degree: | $1536$ |
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 |
---|---|---|---|---|---|---|
8.24.0-4.b.1.5 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.24.0-4.b.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 |
---|---|---|---|---|---|---|
168.96.1-168.n.2.12 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.n.2.18 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bb.1.14 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bb.1.18 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.cy.1.8 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.cy.1.18 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.df.1.8 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.df.1.18 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ea.1.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ea.1.29 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ea.2.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ea.2.29 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.eb.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.eb.1.31 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.eb.2.15 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.eb.2.25 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ec.1.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ec.1.23 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ec.2.15 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ec.2.25 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ed.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ed.1.31 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ed.2.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ed.2.23 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ee.1.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ee.1.29 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ee.2.8 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ee.2.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ef.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ef.1.28 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ef.2.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ef.2.29 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.eg.1.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.eg.1.15 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.eg.2.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.eg.2.15 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.eh.1.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.eh.1.16 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.eh.2.8 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.eh.2.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ey.1.6 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ey.1.20 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ff.1.10 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.ff.1.20 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.fo.1.6 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.fo.1.20 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.fr.1.6 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.fr.1.20 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.144.5-168.h.1.8 | $168$ | $3$ | $3$ | $5$ | $?$ | not computed |
168.192.5-168.h.1.11 | $168$ | $4$ | $4$ | $5$ | $?$ | not computed |
168.384.13-168.h.1.59 | $168$ | $8$ | $8$ | $13$ | $?$ | not computed |