Invariants
| Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $3600$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $17 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $10^{2}\cdot20^{2}\cdot30^{2}\cdot60^{2}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $6$ | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 12$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 12$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 60F17 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.480.17.344 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}16&9\\33&14\end{bmatrix}$, $\begin{bmatrix}20&17\\3&50\end{bmatrix}$, $\begin{bmatrix}41&22\\30&49\end{bmatrix}$, $\begin{bmatrix}46&19\\33&44\end{bmatrix}$, $\begin{bmatrix}50&41\\39&10\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.240.17.my.1 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $12$ |
| Cyclic 60-torsion field degree: | $192$ |
| Full 60-torsion field degree: | $4608$ |
Jacobian
| Conductor: | $2^{43}\cdot3^{25}\cdot5^{34}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{17}$ |
| Newforms: | 50.2.a.b$^{2}$, 75.2.a.a$^{2}$, 75.2.a.b$^{2}$, 150.2.a.b, 3600.2.a.a, 3600.2.a.bb$^{2}$, 3600.2.a.bf$^{2}$, 3600.2.a.bi, 3600.2.a.bl, 3600.2.a.k$^{2}$, 3600.2.a.n |
Rational points
This modular curve has no $\Q_p$ points for $p=7$, 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 |
|---|---|---|---|---|---|---|
| 30.240.7-30.h.1.2 | $30$ | $2$ | $2$ | $7$ | $0$ | $1^{10}$ |
| 60.240.7-30.h.1.14 | $60$ | $2$ | $2$ | $7$ | $0$ | $1^{10}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 60.960.33-60.v.1.12 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{16}$ |
| 60.960.33-60.bj.1.19 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{16}$ |
| 60.960.33-60.cp.1.3 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{16}$ |
| 60.960.33-60.cq.1.3 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{16}$ |
| 60.960.33-60.jn.1.5 | $60$ | $2$ | $2$ | $33$ | $12$ | $1^{16}$ |
| 60.960.33-60.jo.1.11 | $60$ | $2$ | $2$ | $33$ | $15$ | $1^{16}$ |
| 60.960.33-60.jr.1.1 | $60$ | $2$ | $2$ | $33$ | $15$ | $1^{16}$ |
| 60.960.33-60.js.1.4 | $60$ | $2$ | $2$ | $33$ | $12$ | $1^{16}$ |
| 60.960.33-60.mx.1.13 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.my.1.12 | $60$ | $2$ | $2$ | $33$ | $11$ | $1^{16}$ |
| 60.960.33-60.nb.1.2 | $60$ | $2$ | $2$ | $33$ | $11$ | $1^{16}$ |
| 60.960.33-60.nc.1.4 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.nw.1.14 | $60$ | $2$ | $2$ | $33$ | $12$ | $1^{16}$ |
| 60.960.33-60.nx.1.12 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{16}$ |
| 60.960.33-60.oa.1.4 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{16}$ |
| 60.960.33-60.ob.1.3 | $60$ | $2$ | $2$ | $33$ | $12$ | $1^{16}$ |
| 60.960.33-60.ow.1.15 | $60$ | $2$ | $2$ | $33$ | $13$ | $1^{16}$ |
| 60.960.33-60.ox.1.15 | $60$ | $2$ | $2$ | $33$ | $11$ | $1^{16}$ |
| 60.960.33-60.pu.1.15 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{16}$ |
| 60.960.33-60.pv.1.13 | $60$ | $2$ | $2$ | $33$ | $11$ | $1^{16}$ |
| 60.960.33-60.qs.1.15 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{16}$ |
| 60.960.33-60.qt.1.14 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.re.1.15 | $60$ | $2$ | $2$ | $33$ | $12$ | $1^{16}$ |
| 60.960.33-60.rf.1.24 | $60$ | $2$ | $2$ | $33$ | $12$ | $1^{16}$ |
| 60.1440.49-60.btp.1.3 | $60$ | $3$ | $3$ | $49$ | $17$ | $1^{32}$ |
| 60.1440.53-60.dxx.1.6 | $60$ | $3$ | $3$ | $53$ | $17$ | $1^{36}$ |