Invariants
| Level: | $112$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-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 | $8^{12}$ | Cusp orbits | $2^{2}\cdot8$ | ||
| 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: | 8B3 |
Level structure
| $\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}12&3\\81&68\end{bmatrix}$, $\begin{bmatrix}18&97\\5&70\end{bmatrix}$, $\begin{bmatrix}43&12\\20&11\end{bmatrix}$, $\begin{bmatrix}110&13\\47&50\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 112-isogeny field degree: | $32$ |
| Cyclic 112-torsion field degree: | $1536$ |
| Full 112-torsion field degree: | $516096$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 16.48.1.bn.1 | $16$ | $2$ | $2$ | $1$ | $1$ |
| 56.48.1.hq.1 | $56$ | $2$ | $2$ | $1$ | $1$ |
| 112.48.0.cb.2 | $112$ | $2$ | $2$ | $0$ | $?$ |
| 112.48.1.fn.1 | $112$ | $2$ | $2$ | $1$ | $?$ |
| 112.48.2.ca.1 | $112$ | $2$ | $2$ | $2$ | $?$ |
| 112.48.2.dw.1 | $112$ | $2$ | $2$ | $2$ | $?$ |
| 112.48.2.dy.1 | $112$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 112.192.9.sq.1 | $112$ | $2$ | $2$ | $9$ |
| 112.192.9.ta.1 | $112$ | $2$ | $2$ | $9$ |
| 112.192.9.bde.1 | $112$ | $2$ | $2$ | $9$ |
| 112.192.9.bdk.1 | $112$ | $2$ | $2$ | $9$ |