Invariants
Level: | $176$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $2 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 14 }{2}$ | ||||||
Cusps: | $14$ (of which $2$ are rational) | Cusp widths | $4^{8}\cdot8^{4}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2^{4}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16I2 |
Level structure
$\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}7&12\\136&139\end{bmatrix}$, $\begin{bmatrix}87&156\\48&57\end{bmatrix}$, $\begin{bmatrix}105&88\\60&27\end{bmatrix}$, $\begin{bmatrix}111&16\\76&29\end{bmatrix}$, $\begin{bmatrix}169&60\\168&75\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 176.96.2.c.1 for the level structure with $-I$) |
Cyclic 176-isogeny field degree: | $48$ |
Cyclic 176-torsion field degree: | $1920$ |
Full 176-torsion field degree: | $1689600$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
16.96.0-8.c.1.4 | $16$ | $2$ | $2$ | $0$ | $0$ |
88.96.0-8.c.1.4 | $88$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
176.384.5-176.n.1.14 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.n.2.14 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.r.1.16 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.r.2.14 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.bl.1.16 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.bl.2.16 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.bn.1.24 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.bn.3.24 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.cw.1.16 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.cw.2.18 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.cx.1.12 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.cx.2.13 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.db.1.14 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.db.2.16 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.df.1.15 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.df.2.16 | $176$ | $2$ | $2$ | $5$ |
176.384.7-176.k.1.10 | $176$ | $2$ | $2$ | $7$ |
176.384.7-176.m.1.1 | $176$ | $2$ | $2$ | $7$ |
176.384.7-176.o.1.4 | $176$ | $2$ | $2$ | $7$ |
176.384.7-176.p.1.3 | $176$ | $2$ | $2$ | $7$ |
176.384.7-176.ba.1.17 | $176$ | $2$ | $2$ | $7$ |
176.384.7-176.bc.1.13 | $176$ | $2$ | $2$ | $7$ |
176.384.7-176.bg.1.13 | $176$ | $2$ | $2$ | $7$ |
176.384.7-176.bi.1.15 | $176$ | $2$ | $2$ | $7$ |