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 | $2^{4}\cdot8^{2}$ | Cusp orbits | $2^{3}$ | ||
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: | 8G0 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 24.48.0.559 |
Level structure
$\GL_2(\Z/24\Z)$-generators: | $\begin{bmatrix}13&14\\4&13\end{bmatrix}$, $\begin{bmatrix}17&3\\20&19\end{bmatrix}$, $\begin{bmatrix}21&1\\16&1\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 24.24.0.o.1 for the level structure with $-I$) |
Cyclic 24-isogeny field degree: | $8$ |
Cyclic 24-torsion field degree: | $32$ |
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 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 |
---|---|---|---|---|---|
8.24.0-8.d.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
24.24.0-8.d.1.4 | $24$ | $2$ | $2$ | $0$ | $0$ |
24.24.0-24.z.1.6 | $24$ | $2$ | $2$ | $0$ | $0$ |
24.24.0-24.z.1.9 | $24$ | $2$ | $2$ | $0$ | $0$ |
24.24.0-24.bb.1.4 | $24$ | $2$ | $2$ | $0$ | $0$ |
24.24.0-24.bb.1.9 | $24$ | $2$ | $2$ | $0$ | $0$ |
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.co.1.11 | $24$ | $3$ | $3$ | $4$ |
24.192.3-24.cq.1.2 | $24$ | $4$ | $4$ | $3$ |
120.240.8-120.bp.1.3 | $120$ | $5$ | $5$ | $8$ |
120.288.7-120.bni.1.3 | $120$ | $6$ | $6$ | $7$ |
120.480.15-120.fb.1.20 | $120$ | $10$ | $10$ | $15$ |
168.384.11-168.dk.1.14 | $168$ | $8$ | $8$ | $11$ |