Invariants
Level: | $112$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot16^{4}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16M1 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}37&56\\84&13\end{bmatrix}$, $\begin{bmatrix}85&16\\58&17\end{bmatrix}$, $\begin{bmatrix}87&24\\1&101\end{bmatrix}$, $\begin{bmatrix}105&16\\62&17\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 112.96.1.bf.2 for the level structure with $-I$) |
Cyclic 112-isogeny field degree: | $16$ |
Cyclic 112-torsion field degree: | $192$ |
Full 112-torsion field degree: | $258048$ |
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 |
---|---|---|---|---|---|---|
16.96.0-16.j.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
56.96.0-56.bd.1.5 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
112.96.0-16.j.1.7 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-56.bd.1.6 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-112.bk.1.4 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-112.bk.1.9 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-112.bl.1.7 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.0-112.bl.1.9 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.96.1-112.g.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.g.1.16 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bo.1.7 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bo.1.9 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bp.2.7 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.96.1-112.bp.2.9 | $112$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
112.384.5-112.gm.1.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.gn.1.3 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.gq.1.2 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
112.384.5-112.gr.1.1 | $112$ | $2$ | $2$ | $5$ | $?$ | not computed |
224.384.5-224.bc.2.6 | $224$ | $2$ | $2$ | $5$ | $?$ | not computed |
224.384.5-224.bd.2.7 | $224$ | $2$ | $2$ | $5$ | $?$ | not computed |
224.384.5-224.bk.2.6 | $224$ | $2$ | $2$ | $5$ | $?$ | not computed |
224.384.5-224.bn.2.6 | $224$ | $2$ | $2$ | $5$ | $?$ | not computed |
224.384.5-224.ck.2.2 | $224$ | $2$ | $2$ | $5$ | $?$ | not computed |
224.384.5-224.cn.2.2 | $224$ | $2$ | $2$ | $5$ | $?$ | not computed |
224.384.5-224.cu.2.2 | $224$ | $2$ | $2$ | $5$ | $?$ | not computed |
224.384.5-224.cv.2.3 | $224$ | $2$ | $2$ | $5$ | $?$ | not computed |