Invariants
| Level: | $252$ | $\SL_2$-level: | $36$ | Newform level: | $1$ | ||
| Index: | $216$ | $\PSL_2$-index: | $108$ | ||||
| Genus: | $4 = 1 + \frac{ 108 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $3^{3}\cdot6^{3}\cdot9^{3}\cdot18^{3}$ | Cusp orbits | $3^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 6$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 4$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 18Q4 |
Level structure
| $\GL_2(\Z/252\Z)$-generators: | $\begin{bmatrix}31&54\\4&209\end{bmatrix}$, $\begin{bmatrix}103&44\\58&57\end{bmatrix}$, $\begin{bmatrix}110&97\\29&210\end{bmatrix}$, $\begin{bmatrix}156&205\\187&228\end{bmatrix}$, $\begin{bmatrix}227&210\\36&233\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 126.108.4.e.2 for the level structure with $-I$) |
| Cyclic 252-isogeny field degree: | $48$ |
| Cyclic 252-torsion field degree: | $3456$ |
| Full 252-torsion field degree: | $3483648$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 36.72.2-18.c.1.3 | $36$ | $3$ | $3$ | $2$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.