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: | $\begin{bmatrix}16&81\\17&64\end{bmatrix}$, $\begin{bmatrix}25&4\\108&65\end{bmatrix}$, $\begin{bmatrix}61&12\\58&35\end{bmatrix}$, $\begin{bmatrix}100&103\\29&42\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 112.48.1.bh.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 |
---|---|---|---|---|---|---|
16.48.1-16.a.1.14 | $16$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
56.48.0-56.bv.2.16 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
112.48.0-112.e.1.2 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.48.0-112.e.1.24 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.48.0-56.bv.2.3 | $112$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
112.48.1-16.a.1.16 | $112$ | $2$ | $2$ | $1$ | $?$ | 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.c.2.3 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.s.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.bh.2.5 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.bs.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.ch.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.ci.1.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.cu.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
112.192.1-112.db.2.1 | $112$ | $2$ | $2$ | $1$ | $?$ | dimension zero |