Invariants
Level: | $168$ | $\SL_2$-level: | $12$ | 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 | $12^{6}$ | 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: | 12C4 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}25&74\\124&157\end{bmatrix}$, $\begin{bmatrix}41&158\\26&67\end{bmatrix}$, $\begin{bmatrix}59&84\\72&23\end{bmatrix}$, $\begin{bmatrix}95&108\\24&163\end{bmatrix}$, $\begin{bmatrix}101&98\\16&65\end{bmatrix}$, $\begin{bmatrix}165&70\\146&123\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.72.4.bs.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $128$ |
Cyclic 168-torsion field degree: | $6144$ |
Full 168-torsion field degree: | $1032192$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.72.2-12.a.1.6 | $24$ | $2$ | $2$ | $2$ | $0$ |
84.72.2-12.a.1.8 | $84$ | $2$ | $2$ | $2$ | $?$ |
168.72.2-168.f.1.16 | $168$ | $2$ | $2$ | $2$ | $?$ |
168.72.2-168.f.1.21 | $168$ | $2$ | $2$ | $2$ | $?$ |
168.72.2-168.f.1.26 | $168$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.