Invariants
| Level: | $24$ | $\SL_2$-level: | $8$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $4^{6}$ | Cusp orbits | $2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 4G0 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 24.48.0.494 |
Level structure
| $\GL_2(\Z/24\Z)$-generators: | $\begin{bmatrix}13&18\\10&7\end{bmatrix}$, $\begin{bmatrix}21&4\\10&13\end{bmatrix}$, $\begin{bmatrix}23&0\\10&19\end{bmatrix}$, $\begin{bmatrix}23&10\\6&5\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 12.24.0.a.1 for the level structure with $-I$) |
| Cyclic 24-isogeny field degree: | $16$ |
| Cyclic 24-torsion field degree: | $128$ |
| Full 24-torsion field degree: | $1536$ |
Models
Smooth plane model Smooth plane model
| $ 0 $ | $=$ | $ 16 x^{2} - 3 y^{2} - 3 z^{2} $ |
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 |
|---|---|---|---|---|---|
| 8.24.0-4.a.1.6 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 24.24.0-4.a.1.3 | $24$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.