Invariants
Level: | $112$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (all of which are rational) | Cusp widths | $2^{2}\cdot4\cdot16$ | Cusp orbits | $1^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16A1 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}19&88\\56&43\end{bmatrix}$, $\begin{bmatrix}45&38\\62&61\end{bmatrix}$, $\begin{bmatrix}78&41\\99&56\end{bmatrix}$, $\begin{bmatrix}93&10\\76&31\end{bmatrix}$, $\begin{bmatrix}93&34\\66&53\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 112.24.1.a.1 for the level structure with $-I$) |
Cyclic 112-isogeny field degree: | $16$ |
Cyclic 112-torsion field degree: | $384$ |
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 |
---|---|---|---|---|---|---|
16.24.0-8.n.1.8 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
56.24.0-8.n.1.11 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
112.96.1-112.a.2.6 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.d.1.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.g.1.10 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.i.1.6 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bo.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bo.2.3 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bp.1.5 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bp.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bq.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bq.2.5 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.br.1.5 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.br.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bs.1.5 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bs.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bt.1.3 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bt.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bu.1.5 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bu.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bv.1.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bv.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.cf.1.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.cg.1.2 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.cj.1.4 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.ck.1.10 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.384.13-112.k.1.3 | $112$ | $8$ | $8$ | $13$ | $?$ | not computed |