Invariants
| Level: | $24$ | $\SL_2$-level: | $24$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
| Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $1^{4}\cdot3^{4}\cdot8\cdot24$ | Cusp orbits | $1^{2}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24B0 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 24.48.0.949 |
Level structure
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points, including 8 stored non-cuspidal points.
Modular covers
Cover information
Click on a modular curve in the diagram to see information about it.
|
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.24.0.f.1 | $12$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 24.96.3.bj.1 | $24$ | $2$ | $2$ | $3$ |
| 24.96.3.cm.1 | $24$ | $2$ | $2$ | $3$ |
| 24.96.3.dj.2 | $24$ | $2$ | $2$ | $3$ |
| 24.96.3.dn.2 | $24$ | $2$ | $2$ | $3$ |
| 24.96.3.fh.1 | $24$ | $2$ | $2$ | $3$ |
| 24.96.3.fi.1 | $24$ | $2$ | $2$ | $3$ |
| 24.96.3.fl.1 | $24$ | $2$ | $2$ | $3$ |
| 24.96.3.fm.1 | $24$ | $2$ | $2$ | $3$ |
| 24.144.3.e.1 | $24$ | $3$ | $3$ | $3$ |
| 72.144.3.e.2 | $72$ | $3$ | $3$ | $3$ |
| 72.144.8.e.2 | $72$ | $3$ | $3$ | $8$ |
| 72.144.8.i.2 | $72$ | $3$ | $3$ | $8$ |
| 120.96.3.ms.1 | $120$ | $2$ | $2$ | $3$ |
| 120.96.3.mt.1 | $120$ | $2$ | $2$ | $3$ |
| 120.96.3.mw.2 | $120$ | $2$ | $2$ | $3$ |
| 120.96.3.mx.2 | $120$ | $2$ | $2$ | $3$ |
| 120.96.3.ni.1 | $120$ | $2$ | $2$ | $3$ |
| 120.96.3.nj.1 | $120$ | $2$ | $2$ | $3$ |
| 120.96.3.nm.1 | $120$ | $2$ | $2$ | $3$ |
| 120.96.3.nn.1 | $120$ | $2$ | $2$ | $3$ |
| 120.240.16.fe.1 | $120$ | $5$ | $5$ | $16$ |
| 120.288.15.eke.2 | $120$ | $6$ | $6$ | $15$ |
| 168.96.3.ki.1 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.kj.1 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.km.1 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.kn.1 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.ky.1 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.kz.1 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.lc.2 | $168$ | $2$ | $2$ | $3$ |
| 168.96.3.ld.1 | $168$ | $2$ | $2$ | $3$ |
| 168.384.23.lq.1 | $168$ | $8$ | $8$ | $23$ |
| 264.96.3.ki.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.kj.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.km.2 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.kn.2 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.ky.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.kz.1 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.lc.2 | $264$ | $2$ | $2$ | $3$ |
| 264.96.3.ld.2 | $264$ | $2$ | $2$ | $3$ |
| 312.96.3.ms.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.mt.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.mw.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.mx.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.ni.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.nj.1 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.nm.2 | $312$ | $2$ | $2$ | $3$ |
| 312.96.3.nn.1 | $312$ | $2$ | $2$ | $3$ |