Invariants
| Level: | $112$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $8^{4}\cdot16^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 5$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16D5 |
Level structure
| $\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}1&66\\84&17\end{bmatrix}$, $\begin{bmatrix}11&60\\64&39\end{bmatrix}$, $\begin{bmatrix}55&8\\104&37\end{bmatrix}$, $\begin{bmatrix}101&34\\68&83\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 112.96.5.bq.1 for the level structure with $-I$) |
| Cyclic 112-isogeny field degree: | $32$ |
| Cyclic 112-torsion field degree: | $768$ |
| Full 112-torsion field degree: | $258048$ |
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 |
|---|---|---|---|---|---|
| 8.96.1-8.i.2.5 | $8$ | $2$ | $2$ | $1$ | $0$ |
| 112.96.1-8.i.2.3 | $112$ | $2$ | $2$ | $1$ | $?$ |
| 112.96.3-112.e.2.2 | $112$ | $2$ | $2$ | $3$ | $?$ |
| 112.96.3-112.e.2.21 | $112$ | $2$ | $2$ | $3$ | $?$ |
| 112.96.3-112.f.2.2 | $112$ | $2$ | $2$ | $3$ | $?$ |
| 112.96.3-112.f.2.21 | $112$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 112.384.9-112.da.1.12 | $112$ | $2$ | $2$ | $9$ |
| 112.384.9-112.dk.2.1 | $112$ | $2$ | $2$ | $9$ |
| 112.384.9-112.dr.1.7 | $112$ | $2$ | $2$ | $9$ |
| 112.384.9-112.dz.2.2 | $112$ | $2$ | $2$ | $9$ |
| 112.384.9-112.fk.2.6 | $112$ | $2$ | $2$ | $9$ |
| 112.384.9-112.fs.1.5 | $112$ | $2$ | $2$ | $9$ |
| 112.384.9-112.ga.3.3 | $112$ | $2$ | $2$ | $9$ |
| 112.384.9-112.go.1.13 | $112$ | $2$ | $2$ | $9$ |