Invariants
Level: | $24$ | $\SL_2$-level: | $4$ | ||||
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: | 24.48.0.136 |
Level structure
$\GL_2(\Z/24\Z)$-generators: | $\begin{bmatrix}11&10\\20&23\end{bmatrix}$, $\begin{bmatrix}11&18\\10&13\end{bmatrix}$, $\begin{bmatrix}19&10\\14&7\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 24.24.0.d.1 for the level structure with $-I$) |
Cyclic 24-isogeny field degree: | $16$ |
Cyclic 24-torsion field degree: | $64$ |
Full 24-torsion field degree: | $1536$ |
Models
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 24 x^{2} - y^{2} + y z - 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 |
---|---|---|---|---|---|
8.24.0-8.a.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
12.24.0-12.b.1.1 | $12$ | $2$ | $2$ | $0$ | $0$ |
24.24.0-8.a.1.3 | $24$ | $2$ | $2$ | $0$ | $0$ |
24.24.0-12.b.1.3 | $24$ | $2$ | $2$ | $0$ | $0$ |
24.24.0-24.b.1.2 | $24$ | $2$ | $2$ | $0$ | $0$ |
24.24.0-24.b.1.6 | $24$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
24.144.4-24.g.1.4 | $24$ | $3$ | $3$ | $4$ |
24.192.3-24.be.1.9 | $24$ | $4$ | $4$ | $3$ |
120.240.8-120.d.1.8 | $120$ | $5$ | $5$ | $8$ |
120.288.7-120.cs.1.2 | $120$ | $6$ | $6$ | $7$ |
120.480.15-120.d.1.2 | $120$ | $10$ | $10$ | $15$ |
168.384.11-168.g.1.22 | $168$ | $8$ | $8$ | $11$ |