Invariants
| Level: | $252$ | $\SL_2$-level: | $36$ | Newform level: | $1$ | ||
| Index: | $432$ | $\PSL_2$-index: | $216$ | ||||
| Genus: | $10 = 1 + \frac{ 216 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 18 }{2}$ | ||||||
| Cusps: | $18$ (none of which are rational) | Cusp widths | $3^{6}\cdot9^{6}\cdot12^{3}\cdot36^{3}$ | Cusp orbits | $3^{2}\cdot6^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $5 \le \gamma \le 18$ | ||||||
| $\overline{\Q}$-gonality: | $5 \le \gamma \le 10$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 36S10 |
Level structure
| $\GL_2(\Z/252\Z)$-generators: | $\begin{bmatrix}44&241\\77&102\end{bmatrix}$, $\begin{bmatrix}55&84\\142&233\end{bmatrix}$, $\begin{bmatrix}59&30\\8&187\end{bmatrix}$, $\begin{bmatrix}82&75\\147&100\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 252.216.10.bh.2 for the level structure with $-I$) |
| Cyclic 252-isogeny field degree: | $48$ |
| Cyclic 252-torsion field degree: | $3456$ |
| Full 252-torsion field degree: | $1741824$ |
Rational points
This modular curve has no $\Q_p$ points for $p=37$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 36.144.4-36.n.1.7 | $36$ | $3$ | $3$ | $4$ | $1$ |
| 252.216.4-126.d.1.3 | $252$ | $2$ | $2$ | $4$ | $?$ |
| 252.216.4-126.d.1.11 | $252$ | $2$ | $2$ | $4$ | $?$ |