Invariants
| Level: | $24$ | $\SL_2$-level: | $8$ | ||||
| Index: | $24$ | $\PSL_2$-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: | $1 \le \gamma \le 2$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8G0 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 24.24.0.228 |
Level structure
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points, including 13 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map of degree 24 to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{2^6}{3\cdot5^2}\cdot\frac{(4x+y)^{24}(2368x^{4}+2688x^{3}y+1728x^{2}y^{2}+1008xy^{3}+333y^{4})^{3}(4672x^{4}-8448x^{3}y+6912x^{2}y^{2}-3168xy^{3}+657y^{4})^{3}}{(4x+y)^{24}(8x^{2}-3y^{2})^{2}(8x^{2}-36xy+3y^{2})^{8}(24x^{2}-8xy+9y^{2})^{2}}$ |
Modular covers
Cover information
Click on a modular curve in the diagram to see information about it.
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This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.12.0.m.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 12.12.0.h.1 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 24.12.0.y.1 | $24$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 24.72.4.fc.1 | $24$ | $3$ | $3$ | $4$ |
| 24.96.3.fc.1 | $24$ | $4$ | $4$ | $3$ |
| 120.120.8.de.1 | $120$ | $5$ | $5$ | $8$ |
| 120.144.7.dkp.1 | $120$ | $6$ | $6$ | $7$ |
| 120.240.15.hy.1 | $120$ | $10$ | $10$ | $15$ |
| 168.192.11.hk.1 | $168$ | $8$ | $8$ | $11$ |
| 264.288.19.xv.1 | $264$ | $12$ | $12$ | $19$ |
| 312.336.23.fv.1 | $312$ | $14$ | $14$ | $23$ |