Invariants
Level: | $24$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{2}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8N0 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 24.96.0.211 |
Level structure
$\GL_2(\Z/24\Z)$-generators: | $\begin{bmatrix}9&16\\8&5\end{bmatrix}$, $\begin{bmatrix}13&12\\4&1\end{bmatrix}$, $\begin{bmatrix}13&20\\8&5\end{bmatrix}$, $\begin{bmatrix}13&20\\10&3\end{bmatrix}$, $\begin{bmatrix}19&0\\4&23\end{bmatrix}$ |
$\GL_2(\Z/24\Z)$-subgroup: | $C_2^4\times \GL(2,3)$ |
Contains $-I$: | no $\quad$ (see 24.48.0.c.1 for the level structure with $-I$) |
Cyclic 24-isogeny field degree: | $8$ |
Cyclic 24-torsion field degree: | $32$ |
Full 24-torsion field degree: | $768$ |
Models
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ x^{2} + x z + 3 y^{2} + z^{2} $ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.48.0-4.b.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
12.48.0-4.b.1.1 | $12$ | $2$ | $2$ | $0$ | $0$ |
24.48.0-24.i.1.2 | $24$ | $2$ | $2$ | $0$ | $0$ |
24.48.0-24.i.1.29 | $24$ | $2$ | $2$ | $0$ | $0$ |
24.48.0-24.i.2.2 | $24$ | $2$ | $2$ | $0$ | $0$ |
24.48.0-24.i.2.23 | $24$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.