Invariants
Level: | $176$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{12}\cdot16^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}\cdot8$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16O5 |
Level structure
$\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}65&148\\136&105\end{bmatrix}$, $\begin{bmatrix}73&76\\100&89\end{bmatrix}$, $\begin{bmatrix}87&40\\36&9\end{bmatrix}$, $\begin{bmatrix}141&164\\88&105\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 176.192.5.a.2 for the level structure with $-I$) |
Cyclic 176-isogeny field degree: | $48$ |
Cyclic 176-torsion field degree: | $960$ |
Full 176-torsion field degree: | $844800$ |
Rational points
This modular curve has no $\Q_p$ points for $p=3,31$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
16.192.2-16.a.1.2 | $16$ | $2$ | $2$ | $2$ | $0$ |
88.192.1-88.x.2.5 | $88$ | $2$ | $2$ | $1$ | $?$ |
176.192.1-88.x.2.3 | $176$ | $2$ | $2$ | $1$ | $?$ |
176.192.2-16.a.1.6 | $176$ | $2$ | $2$ | $2$ | $?$ |
176.192.2-176.a.1.1 | $176$ | $2$ | $2$ | $2$ | $?$ |
176.192.2-176.a.1.26 | $176$ | $2$ | $2$ | $2$ | $?$ |