Invariants
Level: | $168$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $2^{4}\cdot6^{4}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $2^{6}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24W3 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}59&52\\90&49\end{bmatrix}$, $\begin{bmatrix}79&114\\70&83\end{bmatrix}$, $\begin{bmatrix}81&28\\158&103\end{bmatrix}$, $\begin{bmatrix}141&134\\146&93\end{bmatrix}$, $\begin{bmatrix}142&95\\145&12\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 168.96.3.qp.1 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $16$ |
Cyclic 168-torsion field degree: | $384$ |
Full 168-torsion field degree: | $774144$ |
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 |
---|---|---|---|---|---|
24.96.1-24.ix.1.22 | $24$ | $2$ | $2$ | $1$ | $0$ |
168.96.0-168.dq.1.50 | $168$ | $2$ | $2$ | $0$ | $?$ |
168.96.0-168.dq.1.52 | $168$ | $2$ | $2$ | $0$ | $?$ |
168.96.1-24.ix.1.19 | $168$ | $2$ | $2$ | $1$ | $?$ |
168.96.2-168.f.1.50 | $168$ | $2$ | $2$ | $2$ | $?$ |
168.96.2-168.f.1.52 | $168$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
168.384.5-168.qv.4.1 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.rk.2.16 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.vf.2.13 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.vh.3.11 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.xh.3.9 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.xk.4.9 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.yv.1.9 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.yy.3.9 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bas.1.11 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bau.1.1 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bbi.3.13 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bbk.4.9 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bde.4.13 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bdg.3.9 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bdu.2.5 | $168$ | $2$ | $2$ | $5$ |
168.384.5-168.bdw.1.9 | $168$ | $2$ | $2$ | $5$ |