Invariants
Level: | $112$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-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: | 16E1 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}1&32\\94&111\end{bmatrix}$, $\begin{bmatrix}35&96\\96&81\end{bmatrix}$, $\begin{bmatrix}37&88\\16&41\end{bmatrix}$, $\begin{bmatrix}79&24\\82&29\end{bmatrix}$, $\begin{bmatrix}79&72\\42&99\end{bmatrix}$, $\begin{bmatrix}93&48\\84&89\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 112.96.1-112.a.2.1, 112.96.1-112.a.2.2, 112.96.1-112.a.2.3, 112.96.1-112.a.2.4, 112.96.1-112.a.2.5, 112.96.1-112.a.2.6, 112.96.1-112.a.2.7, 112.96.1-112.a.2.8, 112.96.1-112.a.2.9, 112.96.1-112.a.2.10, 112.96.1-112.a.2.11, 112.96.1-112.a.2.12, 112.96.1-112.a.2.13, 112.96.1-112.a.2.14, 112.96.1-112.a.2.15, 112.96.1-112.a.2.16, 112.96.1-112.a.2.17, 112.96.1-112.a.2.18, 112.96.1-112.a.2.19, 112.96.1-112.a.2.20, 112.96.1-112.a.2.21, 112.96.1-112.a.2.22, 112.96.1-112.a.2.23, 112.96.1-112.a.2.24 |
Cyclic 112-isogeny field degree: | $16$ |
Cyclic 112-torsion field degree: | $768$ |
Full 112-torsion field degree: | $1032192$ |
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 |
---|---|---|---|---|---|---|
8.24.0.i.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
112.24.0.h.1 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.24.1.a.1 | $112$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
112.96.1.d.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1.d.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1.f.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1.f.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1.m.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1.m.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1.o.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1.o.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.3.bl.2 | $112$ | $2$ | $2$ | $3$ | $?$ | not computed |
112.96.3.bp.1 | $112$ | $2$ | $2$ | $3$ | $?$ | not computed |
112.96.3.bp.2 | $112$ | $2$ | $2$ | $3$ | $?$ | not computed |
112.96.3.br.1 | $112$ | $2$ | $2$ | $3$ | $?$ | not computed |
112.96.3.cc.1 | $112$ | $2$ | $2$ | $3$ | $?$ | not computed |
112.96.3.cg.1 | $112$ | $2$ | $2$ | $3$ | $?$ | not computed |
112.96.3.cg.2 | $112$ | $2$ | $2$ | $3$ | $?$ | not computed |
112.96.3.ci.2 | $112$ | $2$ | $2$ | $3$ | $?$ | not computed |