Invariants
Level: | $176$ | $\SL_2$-level: | $16$ | 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 | $4^{8}\cdot16^{4}$ | Cusp orbits | $2^{4}\cdot4$ | ||
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: | 16J3 |
Level structure
$\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}25&44\\128&85\end{bmatrix}$, $\begin{bmatrix}99&72\\104&105\end{bmatrix}$, $\begin{bmatrix}99&134\\112&53\end{bmatrix}$, $\begin{bmatrix}109&162\\152&53\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 176.96.3.ce.2 for the level structure with $-I$) |
Cyclic 176-isogeny field degree: | $24$ |
Cyclic 176-torsion field degree: | $1920$ |
Full 176-torsion field degree: | $1689600$ |
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 |
---|---|---|---|---|---|
16.96.1-16.a.2.4 | $16$ | $2$ | $2$ | $1$ | $0$ |
88.96.0-88.bb.2.3 | $88$ | $2$ | $2$ | $0$ | $?$ |
176.96.0-88.bb.2.5 | $176$ | $2$ | $2$ | $0$ | $?$ |
176.96.1-16.a.2.10 | $176$ | $2$ | $2$ | $1$ | $?$ |
176.96.2-176.d.1.13 | $176$ | $2$ | $2$ | $2$ | $?$ |
176.96.2-176.d.1.20 | $176$ | $2$ | $2$ | $2$ | $?$ |
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.bg.1.2 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.bi.1.4 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.ed.1.2 | $176$ | $2$ | $2$ | $5$ |
176.384.5-176.ee.1.4 | $176$ | $2$ | $2$ | $5$ |