Invariants
Level: | $176$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}23&68\\136&89\end{bmatrix}$, $\begin{bmatrix}47&60\\172&9\end{bmatrix}$, $\begin{bmatrix}79&92\\116&71\end{bmatrix}$, $\begin{bmatrix}131&76\\140&97\end{bmatrix}$, $\begin{bmatrix}143&120\\144&23\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 88.96.1.w.2 for the level structure with $-I$) |
Cyclic 176-isogeny field degree: | $48$ |
Cyclic 176-torsion field degree: | $1920$ |
Full 176-torsion field degree: | $1689600$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
16.96.0-8.c.1.3 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
176.96.0-8.c.1.1 | $176$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
176.384.5-176.c.2.1 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.c.2.7 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.e.2.3 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.e.2.5 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.n.2.11 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.n.2.12 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.t.2.13 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.t.2.14 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-88.w.1.9 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-88.w.1.15 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-88.y.2.3 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-88.y.2.7 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-88.z.1.3 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-88.z.1.7 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-88.bb.2.9 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-88.bb.2.15 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.co.2.9 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.co.2.12 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.cu.2.10 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.cu.2.11 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.dd.2.1 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.dd.2.4 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.df.2.2 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |
176.384.5-176.df.2.5 | $176$ | $2$ | $2$ | $5$ | $?$ | not computed |