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: | $6$ (none of which are rational) | Cusp widths | $4^{4}\cdot16^{2}$ | Cusp orbits | $2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16C2 |
Level structure
| $\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}7&93\\76&103\end{bmatrix}$, $\begin{bmatrix}39&106\\80&33\end{bmatrix}$, $\begin{bmatrix}61&55\\12&99\end{bmatrix}$, $\begin{bmatrix}81&101\\36&7\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 112.48.2.j.1 for the level structure with $-I$) |
| Cyclic 112-isogeny field degree: | $32$ |
| Cyclic 112-torsion field degree: | $768$ |
| Full 112-torsion field degree: | $516096$ |
Rational points
This modular curve has no $\Q_p$ points for $p=11$, and therefore no 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.y.1.4 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 112.48.0-8.y.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.hl.1.1 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.hm.1.3 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.hp.1.2 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.hq.1.4 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.hr.1.7 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.hs.1.5 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.ht.1.8 | $112$ | $2$ | $2$ | $3$ |
| 112.192.3-112.hu.1.6 | $112$ | $2$ | $2$ | $3$ |