Invariants
| Level: | $24$ | $\SL_2$-level: | $24$ | Newform level: | $576$ | ||
| Index: | $768$ | $\PSL_2$-index: | $384$ | ||||
| Genus: | $17 = 1 + \frac{ 384 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 32 }{2}$ | ||||||
| Cusps: | $32$ (of which $8$ are rational) | Cusp widths | $4^{8}\cdot8^{8}\cdot12^{8}\cdot24^{8}$ | Cusp orbits | $1^{8}\cdot4^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $3$ | ||||||
| $\Q$-gonality: | $6 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $6 \le \gamma \le 8$ | ||||||
| Rational cusps: | $8$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24AO17 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 24.768.17.1033 |
Level structure
| $\GL_2(\Z/24\Z)$-generators: | $\begin{bmatrix}11&16\\0&7\end{bmatrix}$, $\begin{bmatrix}17&8\\0&17\end{bmatrix}$, $\begin{bmatrix}19&12\\0&17\end{bmatrix}$, $\begin{bmatrix}23&2\\0&7\end{bmatrix}$ |
| $\GL_2(\Z/24\Z)$-subgroup: | $D_4\times D_6$ |
| Contains $-I$: | no $\quad$ (see 24.384.17.oi.2 for the level structure with $-I$) |
| Cyclic 24-isogeny field degree: | $1$ |
| Cyclic 24-torsion field degree: | $8$ |
| Full 24-torsion field degree: | $96$ |
Jacobian
| Conductor: | $2^{74}\cdot3^{27}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{9}\cdot2^{4}$ |
| Newforms: | 24.2.a.a$^{2}$, 24.2.d.a$^{2}$, 48.2.a.a, 72.2.d.b, 288.2.d.b, 576.2.a.b, 576.2.a.c$^{2}$, 576.2.a.d, 576.2.a.g, 576.2.a.h |
Rational points
This modular curve has 8 rational cusps but no known non-cuspidal 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.ch.1.2 | $24$ | $4$ | $4$ | $1$ | $1$ | $1^{8}\cdot2^{4}$ |
| 24.384.7-24.bc.2.4 | $24$ | $2$ | $2$ | $7$ | $1$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.bc.2.8 | $24$ | $2$ | $2$ | $7$ | $1$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.bd.2.2 | $24$ | $2$ | $2$ | $7$ | $1$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.bd.2.12 | $24$ | $2$ | $2$ | $7$ | $1$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.dm.1.4 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.dm.1.23 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.dp.2.17 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.dp.2.19 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.9-24.eh.2.8 | $24$ | $2$ | $2$ | $9$ | $2$ | $1^{4}\cdot2^{2}$ |
| 24.384.9-24.eh.2.23 | $24$ | $2$ | $2$ | $9$ | $2$ | $1^{4}\cdot2^{2}$ |
| 24.384.9-24.ei.2.4 | $24$ | $2$ | $2$ | $9$ | $2$ | $1^{4}\cdot2^{2}$ |
| 24.384.9-24.ei.2.23 | $24$ | $2$ | $2$ | $9$ | $2$ | $1^{4}\cdot2^{2}$ |
| 24.384.9-24.ez.1.6 | $24$ | $2$ | $2$ | $9$ | $3$ | $2^{4}$ |
| 24.384.9-24.ez.1.23 | $24$ | $2$ | $2$ | $9$ | $3$ | $2^{4}$ |
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.ix.1.4 | $24$ | $2$ | $2$ | $33$ | $3$ | $2^{6}\cdot4$ |
| 24.1536.33-24.ix.2.3 | $24$ | $2$ | $2$ | $33$ | $3$ | $2^{6}\cdot4$ |
| 24.1536.33-24.jb.2.7 | $24$ | $2$ | $2$ | $33$ | $3$ | $2^{6}\cdot4$ |
| 24.1536.33-24.jb.3.5 | $24$ | $2$ | $2$ | $33$ | $3$ | $2^{6}\cdot4$ |
| 24.1536.33-24.kd.1.3 | $24$ | $2$ | $2$ | $33$ | $3$ | $2^{6}\cdot4$ |
| 24.1536.33-24.kd.4.1 | $24$ | $2$ | $2$ | $33$ | $3$ | $2^{6}\cdot4$ |
| 24.1536.33-24.kh.2.6 | $24$ | $2$ | $2$ | $33$ | $3$ | $2^{6}\cdot4$ |
| 24.1536.33-24.kh.3.3 | $24$ | $2$ | $2$ | $33$ | $3$ | $2^{6}\cdot4$ |
| 24.2304.65-24.xc.1.5 | $24$ | $3$ | $3$ | $65$ | $7$ | $1^{24}\cdot2^{12}$ |
| 48.1536.41-48.nh.2.15 | $48$ | $2$ | $2$ | $41$ | $7$ | $1^{12}\cdot2^{4}\cdot4$ |
| 48.1536.41-48.qb.2.3 | $48$ | $2$ | $2$ | $41$ | $4$ | $1^{12}\cdot2^{4}\cdot4$ |
| 48.1536.41-48.xh.2.5 | $48$ | $2$ | $2$ | $41$ | $3$ | $2^{4}\cdot8^{2}$ |
| 48.1536.41-48.xi.1.5 | $48$ | $2$ | $2$ | $41$ | $3$ | $2^{4}\cdot8^{2}$ |
| 48.1536.41-48.yg.1.4 | $48$ | $2$ | $2$ | $41$ | $3$ | $12^{2}$ |
| 48.1536.41-48.yg.2.4 | $48$ | $2$ | $2$ | $41$ | $3$ | $12^{2}$ |
| 48.1536.41-48.yq.2.7 | $48$ | $2$ | $2$ | $41$ | $3$ | $2^{4}\cdot8^{2}$ |
| 48.1536.41-48.yr.1.5 | $48$ | $2$ | $2$ | $41$ | $3$ | $2^{4}\cdot8^{2}$ |
| 48.1536.41-48.zv.1.23 | $48$ | $2$ | $2$ | $41$ | $3$ | $2^{4}\cdot4^{4}$ |
| 48.1536.41-48.zv.4.15 | $48$ | $2$ | $2$ | $41$ | $3$ | $2^{4}\cdot4^{4}$ |
| 48.1536.41-48.bab.1.4 | $48$ | $2$ | $2$ | $41$ | $3$ | $12^{2}$ |
| 48.1536.41-48.bab.2.4 | $48$ | $2$ | $2$ | $41$ | $3$ | $12^{2}$ |
| 48.1536.41-48.bac.1.4 | $48$ | $2$ | $2$ | $41$ | $3$ | $12^{2}$ |
| 48.1536.41-48.bac.2.4 | $48$ | $2$ | $2$ | $41$ | $3$ | $12^{2}$ |
| 48.1536.41-48.bai.2.8 | $48$ | $2$ | $2$ | $41$ | $3$ | $2^{4}\cdot4^{4}$ |
| 48.1536.41-48.bai.3.8 | $48$ | $2$ | $2$ | $41$ | $3$ | $2^{4}\cdot4^{4}$ |
| 48.1536.41-48.baq.1.7 | $48$ | $2$ | $2$ | $41$ | $3$ | $2^{4}\cdot8^{2}$ |
| 48.1536.41-48.bar.2.5 | $48$ | $2$ | $2$ | $41$ | $3$ | $2^{4}\cdot8^{2}$ |
| 48.1536.41-48.bbp.1.4 | $48$ | $2$ | $2$ | $41$ | $3$ | $12^{2}$ |
| 48.1536.41-48.bbp.2.4 | $48$ | $2$ | $2$ | $41$ | $3$ | $12^{2}$ |
| 48.1536.41-48.bbz.2.7 | $48$ | $2$ | $2$ | $41$ | $3$ | $2^{4}\cdot8^{2}$ |
| 48.1536.41-48.bca.2.7 | $48$ | $2$ | $2$ | $41$ | $3$ | $2^{4}\cdot8^{2}$ |
| 48.1536.41-48.bct.1.16 | $48$ | $2$ | $2$ | $41$ | $7$ | $1^{12}\cdot2^{4}\cdot4$ |
| 48.1536.41-48.bdf.2.7 | $48$ | $2$ | $2$ | $41$ | $4$ | $1^{12}\cdot2^{4}\cdot4$ |