Invariants
| Level: | $24$ | $\SL_2$-level: | $24$ | Newform level: | $288$ | ||
| Index: | $768$ | $\PSL_2$-index: | $384$ | ||||
| Genus: | $17 = 1 + \frac{ 384 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 32 }{2}$ | ||||||
| Cusps: | $32$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}\cdot12^{8}\cdot24^{8}$ | Cusp orbits | $2^{8}\cdot4^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $1$ | ||||||
| $\Q$-gonality: | $6 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $6 \le \gamma \le 8$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24AO17 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 24.768.17.503 |
Level structure
| $\GL_2(\Z/24\Z)$-generators: | $\begin{bmatrix}5&0\\12&7\end{bmatrix}$, $\begin{bmatrix}13&8\\12&17\end{bmatrix}$, $\begin{bmatrix}13&20\\12&23\end{bmatrix}$, $\begin{bmatrix}17&0\\0&11\end{bmatrix}$, $\begin{bmatrix}17&4\\0&11\end{bmatrix}$ |
| $\GL_2(\Z/24\Z)$-subgroup: | $C_2^3\times D_6$ |
| Contains $-I$: | no $\quad$ (see 24.384.17.fl.1 for the level structure with $-I$) |
| Cyclic 24-isogeny field degree: | $2$ |
| Cyclic 24-torsion field degree: | $4$ |
| Full 24-torsion field degree: | $96$ |
Jacobian
| Conductor: | $2^{65}\cdot3^{27}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{9}\cdot2^{4}$ |
| Newforms: | 24.2.a.a$^{2}$, 24.2.d.a, 48.2.a.a, 72.2.a.a, 72.2.d.b$^{2}$, 96.2.d.a, 144.2.a.b, 288.2.a.b, 288.2.a.c, 288.2.a.d$^{2}$ |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=47$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 24.192.1-24.s.1.5 | $24$ | $4$ | $4$ | $1$ | $0$ | $1^{8}\cdot2^{4}$ |
| 24.384.7-24.g.1.1 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.g.1.18 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.h.1.3 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.h.1.7 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.cu.1.4 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.cu.1.25 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.cx.1.4 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.cx.1.29 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.9-24.bk.2.4 | $24$ | $2$ | $2$ | $9$ | $1$ | $2^{4}$ |
| 24.384.9-24.bk.2.33 | $24$ | $2$ | $2$ | $9$ | $1$ | $2^{4}$ |
| 24.384.9-24.dr.2.4 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2^{2}$ |
| 24.384.9-24.dr.2.21 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2^{2}$ |
| 24.384.9-24.ea.1.4 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2^{2}$ |
| 24.384.9-24.ea.1.25 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 24.1536.33-24.bh.1.11 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.33-24.bh.4.5 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.33-24.bj.1.9 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.33-24.bj.4.1 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.33-24.fl.1.7 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.33-24.fl.4.5 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.33-24.fn.1.5 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.33-24.fn.4.1 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.41-24.fi.1.2 | $24$ | $2$ | $2$ | $41$ | $3$ | $1^{12}\cdot2^{4}\cdot4$ |
| 24.1536.41-24.fl.3.2 | $24$ | $2$ | $2$ | $41$ | $4$ | $1^{12}\cdot2^{4}\cdot4$ |
| 24.1536.41-24.fq.1.2 | $24$ | $2$ | $2$ | $41$ | $3$ | $1^{12}\cdot2^{4}\cdot4$ |
| 24.1536.41-24.fr.1.2 | $24$ | $2$ | $2$ | $41$ | $4$ | $1^{12}\cdot2^{4}\cdot4$ |
| 24.1536.41-24.fx.1.2 | $24$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot4^{4}$ |
| 24.1536.41-24.fx.2.2 | $24$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot4^{4}$ |
| 24.1536.41-24.fx.3.2 | $24$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot4^{4}$ |
| 24.1536.41-24.fx.4.2 | $24$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot4^{4}$ |
| 24.2304.65-24.ec.1.16 | $24$ | $3$ | $3$ | $65$ | $3$ | $1^{24}\cdot2^{12}$ |