Invariants
| Level: | $24$ | $\SL_2$-level: | $24$ | Newform level: | $576$ | ||
| Index: | $576$ | $\PSL_2$-index: | $288$ | ||||
| Genus: | $15 = 1 + \frac{ 288 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
| Cusps: | $20$ (none of which are rational) | Cusp widths | $6^{8}\cdot12^{4}\cdot24^{8}$ | Cusp orbits | $2^{2}\cdot4^{4}$ | ||
| 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: | 24E15 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 24.576.15.8769 |
Level structure
| $\GL_2(\Z/24\Z)$-generators: | $\begin{bmatrix}1&16\\16&5\end{bmatrix}$, $\begin{bmatrix}5&2\\8&1\end{bmatrix}$, $\begin{bmatrix}11&14\\4&23\end{bmatrix}$, $\begin{bmatrix}15&20\\8&9\end{bmatrix}$ |
| $\GL_2(\Z/24\Z)$-subgroup: | $D_4\times \SD_{16}$ |
| Contains $-I$: | no $\quad$ (see 24.288.15.jr.1 for the level structure with $-I$) |
| Cyclic 24-isogeny field degree: | $8$ |
| Cyclic 24-torsion field degree: | $16$ |
| Full 24-torsion field degree: | $128$ |
Jacobian
| Conductor: | $2^{52}\cdot3^{27}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{7}\cdot2^{4}$ |
| Newforms: | 24.2.d.a, 36.2.a.a$^{3}$, 72.2.d.a$^{2}$, 72.2.d.b, 144.2.a.a, 192.2.a.d, 576.2.a.b, 576.2.a.d |
Rational points
This modular curve has no $\Q_p$ points for $p=13,19,61$, 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 |
|---|---|---|---|---|---|---|
| 24.288.7-24.fl.2.3 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{4}\cdot2^{2}$ |
| 24.288.7-24.fl.2.14 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{4}\cdot2^{2}$ |
| 24.288.7-24.fm.1.7 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{4}\cdot2^{2}$ |
| 24.288.7-24.fm.1.20 | $24$ | $2$ | $2$ | $7$ | $0$ | $1^{4}\cdot2^{2}$ |
| 24.288.7-24.go.1.2 | $24$ | $2$ | $2$ | $7$ | $1$ | $2^{4}$ |
| 24.288.7-24.go.1.9 | $24$ | $2$ | $2$ | $7$ | $1$ | $2^{4}$ |
| 24.288.8-24.ca.2.1 | $24$ | $2$ | $2$ | $8$ | $1$ | $1^{3}\cdot2^{2}$ |
| 24.288.8-24.ca.2.14 | $24$ | $2$ | $2$ | $8$ | $1$ | $1^{3}\cdot2^{2}$ |
| 24.288.8-24.cb.1.11 | $24$ | $2$ | $2$ | $8$ | $1$ | $1^{3}\cdot2^{2}$ |
| 24.288.8-24.cb.1.14 | $24$ | $2$ | $2$ | $8$ | $1$ | $1^{3}\cdot2^{2}$ |
| 24.288.8-24.el.1.13 | $24$ | $2$ | $2$ | $8$ | $0$ | $1^{3}\cdot2^{2}$ |
| 24.288.8-24.el.1.31 | $24$ | $2$ | $2$ | $8$ | $0$ | $1^{3}\cdot2^{2}$ |
| 24.288.8-24.er.1.11 | $24$ | $2$ | $2$ | $8$ | $0$ | $1^{3}\cdot2^{2}$ |
| 24.288.8-24.er.1.13 | $24$ | $2$ | $2$ | $8$ | $0$ | $1^{3}\cdot2^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 24.1152.33-24.tj.2.1 | $24$ | $2$ | $2$ | $33$ | $3$ | $1^{10}\cdot2^{4}$ |
| 24.1152.33-24.tk.2.1 | $24$ | $2$ | $2$ | $33$ | $4$ | $1^{10}\cdot2^{4}$ |
| 24.1152.33-24.tv.1.9 | $24$ | $2$ | $2$ | $33$ | $3$ | $1^{10}\cdot2^{4}$ |
| 24.1152.33-24.tx.1.5 | $24$ | $2$ | $2$ | $33$ | $4$ | $1^{10}\cdot2^{4}$ |
| 24.1152.33-24.vu.1.5 | $24$ | $2$ | $2$ | $33$ | $2$ | $1^{10}\cdot2^{4}$ |
| 24.1152.33-24.vv.1.5 | $24$ | $2$ | $2$ | $33$ | $4$ | $1^{10}\cdot2^{4}$ |
| 24.1152.33-24.vw.2.1 | $24$ | $2$ | $2$ | $33$ | $2$ | $1^{10}\cdot2^{4}$ |
| 24.1152.33-24.vx.2.1 | $24$ | $2$ | $2$ | $33$ | $4$ | $1^{10}\cdot2^{4}$ |