Invariants
Level: | $112$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $4^{8}\cdot16^{4}$ | Cusp orbits | $2^{2}\cdot8$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16I3 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}49&26\\41&7\end{bmatrix}$, $\begin{bmatrix}75&8\\39&77\end{bmatrix}$, $\begin{bmatrix}79&60\\84&67\end{bmatrix}$, $\begin{bmatrix}93&16\\28&93\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 112-isogeny field degree: | $64$ |
Cyclic 112-torsion field degree: | $3072$ |
Full 112-torsion field degree: | $516096$ |
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 |
---|---|---|---|---|---|
16.48.1.cf.1 | $16$ | $2$ | $2$ | $1$ | $1$ |
56.48.1.jf.1 | $56$ | $2$ | $2$ | $1$ | $1$ |
112.48.0.ce.1 | $112$ | $2$ | $2$ | $0$ | $?$ |
112.48.1.fx.1 | $112$ | $2$ | $2$ | $1$ | $?$ |
112.48.2.ce.2 | $112$ | $2$ | $2$ | $2$ | $?$ |
112.48.2.dl.1 | $112$ | $2$ | $2$ | $2$ | $?$ |
112.48.2.et.1 | $112$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
112.192.9.um.1 | $112$ | $2$ | $2$ | $9$ |
112.192.9.uu.1 | $112$ | $2$ | $2$ | $9$ |
112.192.9.bfo.1 | $112$ | $2$ | $2$ | $9$ |
112.192.9.bfw.1 | $112$ | $2$ | $2$ | $9$ |