Invariants
Level: | $168$ | $\SL_2$-level: | $24$ | 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 $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot3^{2}\cdot6\cdot8\cdot24$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
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: | 24G1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}17&156\\92&13\end{bmatrix}$, $\begin{bmatrix}30&127\\127&54\end{bmatrix}$, $\begin{bmatrix}74&19\\5&84\end{bmatrix}$, $\begin{bmatrix}98&165\\9&158\end{bmatrix}$, $\begin{bmatrix}116&85\\45&28\end{bmatrix}$, $\begin{bmatrix}125&160\\86&111\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.48.1.zw.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $16$ |
Cyclic 168-torsion field degree: | $768$ |
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 |
---|---|---|---|---|---|---|
24.48.0-12.g.1.14 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
84.48.0-12.g.1.7 | $84$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.24.0-168.ba.1.18 | $168$ | $4$ | $4$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
168.192.1-168.rh.1.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.rh.2.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.rh.3.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.rh.4.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.rj.1.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.rj.2.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.rj.3.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.rj.4.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.sr.1.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.sr.2.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.sr.3.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.sr.4.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.st.1.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.st.2.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.st.3.9 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.st.4.17 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.3-168.fb.1.34 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.fv.1.19 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.iq.1.17 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.is.1.25 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.jl.1.10 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.jm.1.9 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.ke.1.10 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.kh.1.9 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.lx.1.10 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.ly.1.17 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.mm.1.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.mp.1.17 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.mv.1.27 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.mw.1.13 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.nw.1.6 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.nz.1.5 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.qc.1.17 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.qc.2.17 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.qc.3.9 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.qc.4.17 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.qe.1.17 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.qe.2.17 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.qe.3.5 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.qe.4.9 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.ra.1.17 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.ra.2.17 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.ra.3.5 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.ra.4.9 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.rc.1.17 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.rc.2.17 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.rc.3.9 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.rc.4.17 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.288.5-168.ph.1.30 | $168$ | $3$ | $3$ | $5$ | $?$ | not computed |