Invariants
Level: | $216$ | $\SL_2$-level: | $108$ | Newform level: | $1$ | ||
Index: | $432$ | $\PSL_2$-index: | $216$ | ||||
Genus: | $16 = 1 + \frac{ 216 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $18^{3}\cdot54^{3}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 16$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 16$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 54E16 |
Level structure
$\GL_2(\Z/216\Z)$-generators: | $\begin{bmatrix}28&117\\187&206\end{bmatrix}$, $\begin{bmatrix}57&124\\4&159\end{bmatrix}$, $\begin{bmatrix}82&177\\93&142\end{bmatrix}$, $\begin{bmatrix}195&68\\202&191\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 108.216.16.s.1 for the level structure with $-I$) |
Cyclic 216-isogeny field degree: | $36$ |
Cyclic 216-torsion field degree: | $2592$ |
Full 216-torsion field degree: | $1119744$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
72.144.4-36.m.1.2 | $72$ | $3$ | $3$ | $4$ | $?$ |
216.216.8-54.a.1.10 | $216$ | $2$ | $2$ | $8$ | $?$ |
216.216.8-54.a.1.15 | $216$ | $2$ | $2$ | $8$ | $?$ |