Invariants
| Level: | $24$ | $\SL_2$-level: | $24$ | Newform level: | $576$ | ||
| Index: | $576$ | $\PSL_2$-index: | $288$ | ||||
| Genus: | $17 = 1 + \frac{ 288 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (none of which are rational) | Cusp widths | $12^{8}\cdot24^{8}$ | Cusp orbits | $2^{2}\cdot4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $1$ | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 6$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 6$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24S17 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 24.576.17.25620 |
Level structure
| $\GL_2(\Z/24\Z)$-generators: | $\begin{bmatrix}1&10\\8&7\end{bmatrix}$, $\begin{bmatrix}15&22\\16&21\end{bmatrix}$, $\begin{bmatrix}19&14\\8&11\end{bmatrix}$, $\begin{bmatrix}23&22\\20&23\end{bmatrix}$ |
| $\GL_2(\Z/24\Z)$-subgroup: | $D_4\times \SD_{16}$ |
| Contains $-I$: | no $\quad$ (see 24.288.17.bqf.1 for the level structure with $-I$) |
| Cyclic 24-isogeny field degree: | $8$ |
| Cyclic 24-torsion field degree: | $32$ |
| Full 24-torsion field degree: | $128$ |
Jacobian
| Conductor: | $2^{68}\cdot3^{30}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{9}\cdot2^{4}$ |
| Newforms: | 36.2.a.a$^{3}$, 72.2.d.a$^{2}$, 72.2.d.b, 96.2.d.a, 144.2.a.a, 192.2.a.b, 192.2.a.d, 576.2.a.c, 576.2.a.g, 576.2.a.h |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=5,47$, 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 |
|---|---|---|---|---|---|---|
| 24.288.8-24.cy.1.18 | $24$ | $2$ | $2$ | $8$ | $0$ | $1^{5}\cdot2^{2}$ |
| 24.288.8-24.cy.1.27 | $24$ | $2$ | $2$ | $8$ | $0$ | $1^{5}\cdot2^{2}$ |
| 24.288.8-24.db.2.19 | $24$ | $2$ | $2$ | $8$ | $0$ | $1^{5}\cdot2^{2}$ |
| 24.288.8-24.db.2.30 | $24$ | $2$ | $2$ | $8$ | $0$ | $1^{5}\cdot2^{2}$ |
| 24.288.8-24.en.2.24 | $24$ | $2$ | $2$ | $8$ | $0$ | $1^{5}\cdot2^{2}$ |
| 24.288.8-24.en.2.25 | $24$ | $2$ | $2$ | $8$ | $0$ | $1^{5}\cdot2^{2}$ |
| 24.288.8-24.er.1.3 | $24$ | $2$ | $2$ | $8$ | $0$ | $1^{5}\cdot2^{2}$ |
| 24.288.8-24.er.1.28 | $24$ | $2$ | $2$ | $8$ | $0$ | $1^{5}\cdot2^{2}$ |
| 24.288.9-24.kj.2.20 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2^{2}$ |
| 24.288.9-24.kj.2.30 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2^{2}$ |
| 24.288.9-24.kk.1.20 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2^{2}$ |
| 24.288.9-24.kk.1.21 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2^{2}$ |
| 24.288.9-24.lp.1.22 | $24$ | $2$ | $2$ | $9$ | $1$ | $2^{4}$ |
| 24.288.9-24.lp.1.28 | $24$ | $2$ | $2$ | $9$ | $1$ | $2^{4}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 24.1152.33-24.hu.2.3 | $24$ | $2$ | $2$ | $33$ | $3$ | $1^{8}\cdot2^{4}$ |
| 24.1152.33-24.ja.2.7 | $24$ | $2$ | $2$ | $33$ | $2$ | $1^{8}\cdot2^{4}$ |
| 24.1152.33-24.of.2.4 | $24$ | $2$ | $2$ | $33$ | $3$ | $1^{8}\cdot2^{4}$ |
| 24.1152.33-24.qb.1.10 | $24$ | $2$ | $2$ | $33$ | $3$ | $1^{8}\cdot2^{4}$ |
| 24.1152.33-24.tj.2.3 | $24$ | $2$ | $2$ | $33$ | $3$ | $1^{8}\cdot2^{4}$ |
| 24.1152.33-24.vl.2.4 | $24$ | $2$ | $2$ | $33$ | $3$ | $1^{8}\cdot2^{4}$ |
| 24.1152.33-24.ym.1.3 | $24$ | $2$ | $2$ | $33$ | $2$ | $1^{8}\cdot2^{4}$ |
| 24.1152.33-24.bbf.1.4 | $24$ | $2$ | $2$ | $33$ | $2$ | $1^{8}\cdot2^{4}$ |