Invariants
Level: | $112$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $8^{4}\cdot16^{4}$ | Cusp orbits | $2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16D5 |
Level structure
$\GL_2(\Z/112\Z)$-generators: | $\begin{bmatrix}15&90\\60&103\end{bmatrix}$, $\begin{bmatrix}23&29\\62&27\end{bmatrix}$, $\begin{bmatrix}47&87\\66&47\end{bmatrix}$, $\begin{bmatrix}87&8\\60&65\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 112.192.5-112.jo.2.1, 112.192.5-112.jo.2.2, 112.192.5-112.jo.2.3, 112.192.5-112.jo.2.4 |
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 |
---|---|---|---|---|---|
16.48.3.bw.2 | $16$ | $2$ | $2$ | $3$ | $1$ |
56.48.1.it.2 | $56$ | $2$ | $2$ | $1$ | $1$ |
112.48.1.hh.2 | $112$ | $2$ | $2$ | $1$ | $?$ |
112.48.1.hn.1 | $112$ | $2$ | $2$ | $1$ | $?$ |
112.48.3.bk.2 | $112$ | $2$ | $2$ | $3$ | $?$ |
112.48.3.bu.1 | $112$ | $2$ | $2$ | $3$ | $?$ |
112.48.3.du.1 | $112$ | $2$ | $2$ | $3$ | $?$ |