Invariants
| Level: | $168$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $4 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $6^{4}\cdot24^{2}$ | Cusp orbits | $2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 6$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 4$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24D4 |
Level structure
| $\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}29&167\\20&55\end{bmatrix}$, $\begin{bmatrix}33&167\\112&99\end{bmatrix}$, $\begin{bmatrix}53&37\\16&93\end{bmatrix}$, $\begin{bmatrix}69&88\\56&27\end{bmatrix}$, $\begin{bmatrix}77&81\\104&157\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 168.72.4.lo.1 for the level structure with $-I$) |
| Cyclic 168-isogeny field degree: | $64$ |
| Cyclic 168-torsion field degree: | $1536$ |
| Full 168-torsion field degree: | $1032192$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 24.72.2-24.ck.1.26 | $24$ | $2$ | $2$ | $2$ | $0$ |
| 84.72.2-84.w.1.1 | $84$ | $2$ | $2$ | $2$ | $?$ |
| 168.48.0-168.di.1.6 | $168$ | $3$ | $3$ | $0$ | $?$ |
| 168.72.2-84.w.1.15 | $168$ | $2$ | $2$ | $2$ | $?$ |
| 168.72.2-24.ck.1.21 | $168$ | $2$ | $2$ | $2$ | $?$ |
| 168.72.2-168.dj.1.6 | $168$ | $2$ | $2$ | $2$ | $?$ |
| 168.72.2-168.dj.1.15 | $168$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 168.288.7-168.doa.1.2 | $168$ | $2$ | $2$ | $7$ |
| 168.288.7-168.doc.1.2 | $168$ | $2$ | $2$ | $7$ |
| 168.288.7-168.doq.1.2 | $168$ | $2$ | $2$ | $7$ |
| 168.288.7-168.dos.1.2 | $168$ | $2$ | $2$ | $7$ |
| 168.288.7-168.dym.1.2 | $168$ | $2$ | $2$ | $7$ |
| 168.288.7-168.dyo.1.2 | $168$ | $2$ | $2$ | $7$ |
| 168.288.7-168.dzk.1.2 | $168$ | $2$ | $2$ | $7$ |
| 168.288.7-168.dzm.1.2 | $168$ | $2$ | $2$ | $7$ |
| 168.288.7-168.eiy.1.2 | $168$ | $2$ | $2$ | $7$ |
| 168.288.7-168.eja.1.2 | $168$ | $2$ | $2$ | $7$ |
| 168.288.7-168.ejo.1.2 | $168$ | $2$ | $2$ | $7$ |
| 168.288.7-168.ejq.1.2 | $168$ | $2$ | $2$ | $7$ |
| 168.288.7-168.esu.1.2 | $168$ | $2$ | $2$ | $7$ |
| 168.288.7-168.esw.1.2 | $168$ | $2$ | $2$ | $7$ |
| 168.288.7-168.etk.1.2 | $168$ | $2$ | $2$ | $7$ |
| 168.288.7-168.etm.1.2 | $168$ | $2$ | $2$ | $7$ |