Invariants
| Level: | $112$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $4$ are rational) | Cusp widths | $4^{4}\cdot16^{2}$ | Cusp orbits | $1^{4}\cdot2$ | ||
| 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: | 16C2 |
Level structure
| $\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}15&16\\52&77\end{bmatrix}$, $\begin{bmatrix}15&60\\68&25\end{bmatrix}$, $\begin{bmatrix}27&40\\36&85\end{bmatrix}$, $\begin{bmatrix}31&34\\52&29\end{bmatrix}$, $\begin{bmatrix}97&18\\40&49\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 112.48.2.d.2 for the level structure with $-I$) |
| Cyclic 112-isogeny field degree: | $16$ |
| Cyclic 112-torsion field degree: | $768$ |
| Full 112-torsion field degree: | $516096$ |
Rational points
This modular curve has 4 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 |
|---|---|---|---|---|---|
| 8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 112.48.0-8.i.1.5 | $112$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 112.192.3-112.bm.1.4 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.bw.2.2 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.ca.1.10 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.cd.1.11 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.ce.2.10 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.cf.2.2 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.cg.1.14 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.ch.1.20 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.cj.2.11 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.ck.1.7 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.cl.2.1 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.cm.2.9 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.cn.1.5 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.co.1.9 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.cu.1.6 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.cv.2.4 | $112$ | $2$ | $2$ | $3$ |