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: | $5 \le \gamma \le 16$ | ||||||
| $\overline{\Q}$-gonality: | $5 \le \gamma \le 16$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 54F16 |
Level structure
| $\GL_2(\Z/216\Z)$-generators: | $\begin{bmatrix}7&152\\166&207\end{bmatrix}$, $\begin{bmatrix}79&62\\48&5\end{bmatrix}$, $\begin{bmatrix}189&20\\74&3\end{bmatrix}$, $\begin{bmatrix}212&133\\137&30\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 108.216.16.t.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.b.1.12 | $216$ | $2$ | $2$ | $8$ | $?$ |
| 216.216.8-54.b.1.14 | $216$ | $2$ | $2$ | $8$ | $?$ |