Invariants
| Level: | $176$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (all of which are rational) | Cusp widths | $2^{2}\cdot4\cdot16$ | Cusp orbits | $1^{4}$ | ||
| 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: | 16A1 |
Level structure
| $\GL_2(\Z/176\Z)$-generators: | $\begin{bmatrix}9&116\\166&115\end{bmatrix}$, $\begin{bmatrix}35&4\\26&169\end{bmatrix}$, $\begin{bmatrix}38&85\\101&94\end{bmatrix}$, $\begin{bmatrix}41&108\\104&133\end{bmatrix}$, $\begin{bmatrix}68&3\\173&158\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 176.24.1.a.1 for the level structure with $-I$) |
| Cyclic 176-isogeny field degree: | $24$ |
| Cyclic 176-torsion field degree: | $960$ |
| Full 176-torsion field degree: | $6758400$ |
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 |
|---|---|---|---|---|---|---|
| 16.24.0-8.n.1.8 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 88.24.0-8.n.1.6 | $88$ | $2$ | $2$ | $0$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 176.96.1-176.a.2.6 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.d.1.2 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.g.1.10 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.i.1.10 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.bo.1.1 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.bo.2.3 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.bp.1.5 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.bp.2.1 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.bq.1.1 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.bq.2.5 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.br.1.5 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.br.2.1 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.bs.1.5 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.bs.2.1 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.bt.1.3 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.bt.2.1 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.bu.1.5 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.bu.2.1 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.bv.1.2 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.bv.2.1 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.cf.1.2 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.cg.1.2 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.cj.1.6 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 176.96.1-176.ck.1.6 | $176$ | $2$ | $2$ | $1$ | $?$ | dimension zero |