Invariants
Level: | $112$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16G1 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}0&73\\43&106\end{bmatrix}$, $\begin{bmatrix}33&38\\100&63\end{bmatrix}$, $\begin{bmatrix}47&10\\0&29\end{bmatrix}$, $\begin{bmatrix}96&81\\79&86\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 112.48.1.by.2 for the level structure with $-I$) |
Cyclic 112-isogeny field degree: | $16$ |
Cyclic 112-torsion field degree: | $384$ |
Full 112-torsion field degree: | $516096$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
16.48.0-8.ba.1.8 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
56.48.0-8.ba.1.2 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
112.48.0-112.e.1.2 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.48.0-112.e.1.18 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.48.1-112.b.1.4 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.48.1-112.b.1.9 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
112.192.1-112.g.1.3 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.z.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.bj.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.bx.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.dm.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.dw.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.ea.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.eo.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |