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: | $32$ (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: | $1$ | ||||||
| $\Q$-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: | 24.768.17.780 |
Level structure
| $\GL_2(\Z/24\Z)$-generators: | $\begin{bmatrix}1&6\\0&19\end{bmatrix}$, $\begin{bmatrix}1&18\\0&19\end{bmatrix}$, $\begin{bmatrix}11&20\\12&7\end{bmatrix}$, $\begin{bmatrix}17&10\\0&23\end{bmatrix}$, $\begin{bmatrix}17&22\\0&11\end{bmatrix}$ |
| $\GL_2(\Z/24\Z)$-subgroup: | $C_2^3\times D_6$ |
| Contains $-I$: | no $\quad$ (see 24.384.17.fv.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$^{2}$, 48.2.a.a, 72.2.a.a, 72.2.d.b, 144.2.a.b, 288.2.a.b, 288.2.a.c, 288.2.a.d$^{2}$, 288.2.d.b |
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.x.2.4 | $24$ | $4$ | $4$ | $1$ | $0$ | $1^{8}\cdot2^{4}$ |
| 24.384.7-24.f.1.1 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.f.1.7 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.i.1.3 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.i.1.33 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.cw.1.2 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.cw.1.27 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.cx.1.2 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.7-24.cx.1.15 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{6}\cdot2^{2}$ |
| 24.384.9-24.bk.2.33 | $24$ | $2$ | $2$ | $9$ | $1$ | $2^{4}$ |
| 24.384.9-24.bk.2.34 | $24$ | $2$ | $2$ | $9$ | $1$ | $2^{4}$ |
| 24.384.9-24.dz.1.9 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2^{2}$ |
| 24.384.9-24.dz.1.20 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2^{2}$ |
| 24.384.9-24.ea.1.13 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2^{2}$ |
| 24.384.9-24.ea.1.20 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2^{2}$ |
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.bs.3.6 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.33-24.bs.4.3 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.33-24.bw.3.3 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.33-24.bw.4.1 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.33-24.fw.3.7 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.33-24.fw.4.5 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.33-24.ga.3.3 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.33-24.ga.4.1 | $24$ | $2$ | $2$ | $33$ | $1$ | $2^{6}\cdot4$ |
| 24.1536.41-24.gc.1.2 | $24$ | $2$ | $2$ | $41$ | $3$ | $1^{12}\cdot2^{4}\cdot4$ |
| 24.1536.41-24.ge.1.2 | $24$ | $2$ | $2$ | $41$ | $4$ | $1^{12}\cdot2^{4}\cdot4$ |
| 24.1536.41-24.gj.1.2 | $24$ | $2$ | $2$ | $41$ | $3$ | $1^{12}\cdot2^{4}\cdot4$ |
| 24.1536.41-24.gl.3.2 | $24$ | $2$ | $2$ | $41$ | $4$ | $1^{12}\cdot2^{4}\cdot4$ |
| 24.1536.41-24.gq.1.9 | $24$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot4^{4}$ |
| 24.1536.41-24.gq.2.9 | $24$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot4^{4}$ |
| 24.1536.41-24.gq.3.2 | $24$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot4^{4}$ |
| 24.1536.41-24.gq.4.3 | $24$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot4^{4}$ |
| 24.2304.65-24.gi.2.9 | $24$ | $3$ | $3$ | $65$ | $3$ | $1^{24}\cdot2^{12}$ |
| 48.1536.41-48.eh.1.20 | $48$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot8^{2}$ |
| 48.1536.41-48.en.1.22 | $48$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot8^{2}$ |
| 48.1536.41-48.gw.1.19 | $48$ | $2$ | $2$ | $41$ | $1$ | $12^{2}$ |
| 48.1536.41-48.hm.1.19 | $48$ | $2$ | $2$ | $41$ | $1$ | $12^{2}$ |
| 48.1536.41-48.ke.1.2 | $48$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot8^{2}$ |
| 48.1536.41-48.kg.1.2 | $48$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot8^{2}$ |
| 48.1536.41-48.mx.1.18 | $48$ | $2$ | $2$ | $41$ | $1$ | $12^{2}$ |
| 48.1536.41-48.mx.2.4 | $48$ | $2$ | $2$ | $41$ | $1$ | $12^{2}$ |
| 48.1536.41-48.mz.1.18 | $48$ | $2$ | $2$ | $41$ | $1$ | $12^{2}$ |
| 48.1536.41-48.mz.2.4 | $48$ | $2$ | $2$ | $41$ | $1$ | $12^{2}$ |
| 48.1536.41-48.qk.1.18 | $48$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot8^{2}$ |
| 48.1536.41-48.qm.1.18 | $48$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot8^{2}$ |
| 48.1536.41-48.ri.1.18 | $48$ | $2$ | $2$ | $41$ | $1$ | $12^{2}$ |
| 48.1536.41-48.ry.1.18 | $48$ | $2$ | $2$ | $41$ | $1$ | $12^{2}$ |
| 48.1536.41-48.tz.1.18 | $48$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot8^{2}$ |
| 48.1536.41-48.uf.1.18 | $48$ | $2$ | $2$ | $41$ | $1$ | $2^{4}\cdot8^{2}$ |