Invariants
Level: | $168$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
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: | 8G1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}13&64\\152&75\end{bmatrix}$, $\begin{bmatrix}15&92\\28&163\end{bmatrix}$, $\begin{bmatrix}37&120\\0&137\end{bmatrix}$, $\begin{bmatrix}105&20\\104&129\end{bmatrix}$, $\begin{bmatrix}145&26\\4&99\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.48.1.ef.2 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $64$ |
Cyclic 168-torsion field degree: | $3072$ |
Full 168-torsion field degree: | $1548288$ |
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 |
---|---|---|---|---|---|---|
8.48.0-8.e.1.15 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.48.0-8.e.1.3 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.0-168.t.1.2 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.0-168.t.1.36 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.1-168.d.1.8 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.48.1-168.d.1.35 | $168$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
168.192.1-168.ba.2.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.cy.1.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.ep.1.12 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.ex.2.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.ii.1.10 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.iq.2.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.kf.2.10 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.kn.1.12 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.me.2.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.mm.1.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.ob.1.15 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.oj.2.7 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.pg.1.10 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.po.2.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.qb.2.11 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.qf.1.14 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.288.9-168.tn.2.34 | $168$ | $3$ | $3$ | $9$ | $?$ | not computed |
168.384.9-168.kp.2.39 | $168$ | $4$ | $4$ | $9$ | $?$ | not computed |