Invariants
| Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $1800$ | ||
| Index: | $576$ | $\PSL_2$-index: | $288$ | ||||
| Genus: | $17 = 1 + \frac{ 288 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (of which $8$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot10^{2}\cdot12^{2}\cdot20^{2}\cdot30^{2}\cdot60^{2}$ | Cusp orbits | $1^{8}\cdot2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $3$ | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 8$ | ||||||
| Rational cusps: | $8$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 60Q17 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.576.17.496 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}13&45\\50&59\end{bmatrix}$, $\begin{bmatrix}41&15\\22&29\end{bmatrix}$, $\begin{bmatrix}53&15\\46&19\end{bmatrix}$, $\begin{bmatrix}59&30\\54&31\end{bmatrix}$, $\begin{bmatrix}59&45\\24&19\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.288.17.im.2 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $2$ |
| Cyclic 60-torsion field degree: | $16$ |
| Full 60-torsion field degree: | $3840$ |
Jacobian
| Conductor: | $2^{39}\cdot3^{29}\cdot5^{23}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{9}\cdot2^{4}$ |
| Newforms: | 15.2.a.a$^{2}$, 30.2.a.a, 30.2.c.a, 360.2.f.a, 360.2.f.c$^{2}$, 1800.2.a.c, 1800.2.a.m$^{2}$, 1800.2.a.n, 1800.2.a.v$^{2}$ |
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 |
|---|---|---|---|---|---|---|
| 30.288.5-30.a.1.16 | $30$ | $2$ | $2$ | $5$ | $0$ | $1^{6}\cdot2^{3}$ |
| 60.144.3-60.xu.2.15 | $60$ | $4$ | $4$ | $3$ | $0$ | $1^{8}\cdot2^{3}$ |
| 60.288.5-30.a.1.11 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{6}\cdot2^{3}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 60.1152.33-60.bh.2.8 | $60$ | $2$ | $2$ | $33$ | $5$ | $1^{8}\cdot2^{4}$ |
| 60.1152.33-60.cy.2.11 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{8}\cdot2^{4}$ |
| 60.1152.33-60.fr.2.7 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{8}\cdot2^{4}$ |
| 60.1152.33-60.ft.2.5 | $60$ | $2$ | $2$ | $33$ | $5$ | $1^{8}\cdot2^{4}$ |
| 60.1152.33-60.hn.2.4 | $60$ | $2$ | $2$ | $33$ | $3$ | $1^{8}\cdot2^{4}$ |
| 60.1152.33-60.hp.2.7 | $60$ | $2$ | $2$ | $33$ | $5$ | $1^{8}\cdot2^{4}$ |
| 60.1152.33-60.if.2.7 | $60$ | $2$ | $2$ | $33$ | $5$ | $1^{8}\cdot2^{4}$ |
| 60.1152.33-60.ij.2.1 | $60$ | $2$ | $2$ | $33$ | $3$ | $1^{8}\cdot2^{4}$ |
| 60.1152.33-60.pl.1.4 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1152.33-60.pl.2.4 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1152.33-60.pm.1.4 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1152.33-60.pm.2.4 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1152.33-60.pp.1.2 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1152.33-60.pp.2.2 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1152.33-60.pq.1.2 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1152.33-60.pq.2.2 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1152.33-60.qr.1.16 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1152.33-60.qr.2.16 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1152.33-60.qs.1.16 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1152.33-60.qs.2.16 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1152.33-60.qv.1.15 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1152.33-60.qv.2.15 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1152.33-60.qw.1.15 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1152.33-60.qw.2.15 | $60$ | $2$ | $2$ | $33$ | $3$ | $4^{4}$ |
| 60.1728.57-60.css.2.23 | $60$ | $3$ | $3$ | $57$ | $8$ | $1^{20}\cdot2^{10}$ |
| 60.2880.97-60.bql.1.9 | $60$ | $5$ | $5$ | $97$ | $16$ | $1^{40}\cdot2^{20}$ |