Invariants
Level: | $176$ | $\SL_2$-level: | $16$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $1^{4}\cdot2^{2}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16H0 |
Level structure
$\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}34&103\\13&28\end{bmatrix}$, $\begin{bmatrix}111&158\\100&57\end{bmatrix}$, $\begin{bmatrix}119&134\\10&99\end{bmatrix}$, $\begin{bmatrix}162&159\\97&80\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 176.48.0.bu.1 for the level structure with $-I$) |
Cyclic 176-isogeny field degree: | $12$ |
Cyclic 176-torsion field degree: | $480$ |
Full 176-torsion field degree: | $3379200$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
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 |
---|---|---|---|---|---|
16.48.0-16.g.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ |
88.48.0-88.bu.2.6 | $88$ | $2$ | $2$ | $0$ | $?$ |
176.48.0-176.f.2.5 | $176$ | $2$ | $2$ | $0$ | $?$ |
176.48.0-176.f.2.14 | $176$ | $2$ | $2$ | $0$ | $?$ |
176.48.0-16.g.1.7 | $176$ | $2$ | $2$ | $0$ | $?$ |
176.48.0-88.bu.2.14 | $176$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
176.192.1-176.j.1.5 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.t.1.5 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.bo.2.5 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.br.2.3 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.dk.1.5 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.dr.1.5 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.ed.2.5 | $176$ | $2$ | $2$ | $1$ |
176.192.1-176.ee.1.2 | $176$ | $2$ | $2$ | $1$ |