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: | $8$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16G1 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}54&17\\109&42\end{bmatrix}$, $\begin{bmatrix}59&80\\50&109\end{bmatrix}$, $\begin{bmatrix}76&101\\31&30\end{bmatrix}$, $\begin{bmatrix}106&101\\71&28\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 112.48.1.bo.1 for the level structure with $-I$) |
Cyclic 112-isogeny field degree: | $16$ |
Cyclic 112-torsion field degree: | $192$ |
Full 112-torsion field degree: | $516096$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
16.48.0-16.e.1.1 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
56.48.0-56.bu.1.15 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
112.48.0-16.e.1.5 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.48.0-56.bu.1.1 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.48.1-112.a.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.48.1-112.a.1.31 | $112$ | $2$ | $2$ | $1$ | $?$ | 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.m.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.u.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.bf.2.5 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.bv.1.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.dp.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.ds.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.ee.2.3 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.ej.2.5 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |