Invariants
Level: | $24$ | $\SL_2$-level: | $24$ | Newform level: | $576$ | ||
Index: | $288$ | $\PSL_2$-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 | $4^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | $2$ | ||||||
$\Q$-gonality: | $6 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $6$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24B17 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 24.288.17.747 |
Level structure
$\GL_2(\Z/24\Z)$-generators: | $\begin{bmatrix}1&6\\12&7\end{bmatrix}$, $\begin{bmatrix}5&4\\20&5\end{bmatrix}$, $\begin{bmatrix}5&6\\0&19\end{bmatrix}$, $\begin{bmatrix}7&20\\16&13\end{bmatrix}$, $\begin{bmatrix}21&20\\4&15\end{bmatrix}$ |
$\GL_2(\Z/24\Z)$-subgroup: | $C_4.D_4^2$ |
Contains $-I$: | yes |
Quadratic refinements: | 24.576.17-24.sr.1.1, 24.576.17-24.sr.1.2, 24.576.17-24.sr.1.3, 24.576.17-24.sr.1.4, 24.576.17-24.sr.1.5, 24.576.17-24.sr.1.6, 24.576.17-24.sr.1.7, 24.576.17-24.sr.1.8, 24.576.17-24.sr.1.9, 24.576.17-24.sr.1.10, 24.576.17-24.sr.1.11, 24.576.17-24.sr.1.12, 24.576.17-24.sr.1.13, 24.576.17-24.sr.1.14, 24.576.17-24.sr.1.15, 24.576.17-24.sr.1.16 |
Cyclic 24-isogeny field degree: | $8$ |
Cyclic 24-torsion field degree: | $64$ |
Full 24-torsion field degree: | $256$ |
Jacobian
Conductor: | $2^{76}\cdot3^{34}$ |
Simple: | no |
Squarefree: | no |
Decomposition: | $1^{9}\cdot2^{4}$ |
Newforms: | 36.2.a.a$^{3}$, 72.2.d.a, 144.2.a.a, 288.2.d.a$^{3}$, 576.2.a.a, 576.2.a.c, 576.2.a.e, 576.2.a.f, 576.2.a.i |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=31,127$, 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 |
---|---|---|---|---|---|---|
24.96.1.bj.2 | $24$ | $3$ | $3$ | $1$ | $1$ | $1^{8}\cdot2^{4}$ |
24.144.8.m.1 | $24$ | $2$ | $2$ | $8$ | $1$ | $1^{5}\cdot2^{2}$ |
24.144.8.s.1 | $24$ | $2$ | $2$ | $8$ | $1$ | $1^{5}\cdot2^{2}$ |
24.144.8.ek.1 | $24$ | $2$ | $2$ | $8$ | $0$ | $1^{5}\cdot2^{2}$ |
24.144.8.em.1 | $24$ | $2$ | $2$ | $8$ | $0$ | $1^{5}\cdot2^{2}$ |
24.144.9.er.1 | $24$ | $2$ | $2$ | $9$ | $2$ | $2^{4}$ |
24.144.9.gy.1 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2^{2}$ |
24.144.9.ha.2 | $24$ | $2$ | $2$ | $9$ | $1$ | $1^{4}\cdot2^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
24.576.33.iv.1 | $24$ | $2$ | $2$ | $33$ | $4$ | $1^{8}\cdot2^{4}$ |
24.576.33.jh.1 | $24$ | $2$ | $2$ | $33$ | $3$ | $1^{8}\cdot2^{4}$ |
24.576.33.pv.2 | $24$ | $2$ | $2$ | $33$ | $3$ | $1^{8}\cdot2^{4}$ |
24.576.33.rd.2 | $24$ | $2$ | $2$ | $33$ | $4$ | $1^{8}\cdot2^{4}$ |
24.576.33.vf.1 | $24$ | $2$ | $2$ | $33$ | $3$ | $1^{8}\cdot2^{4}$ |
24.576.33.vr.1 | $24$ | $2$ | $2$ | $33$ | $4$ | $1^{8}\cdot2^{4}$ |
24.576.33.bbc.2 | $24$ | $2$ | $2$ | $33$ | $4$ | $1^{8}\cdot2^{4}$ |
24.576.33.bbu.2 | $24$ | $2$ | $2$ | $33$ | $2$ | $1^{8}\cdot2^{4}$ |