Invariants
| Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $1200$ | ||
| 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: | $3$ | ||||||
| $\Q$-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: | 60.480.17.360 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}1&4\\24&49\end{bmatrix}$, $\begin{bmatrix}1&59\\24&19\end{bmatrix}$, $\begin{bmatrix}43&1\\6&11\end{bmatrix}$, $\begin{bmatrix}43&45\\24&47\end{bmatrix}$, $\begin{bmatrix}47&16\\0&53\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.240.17.mw.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: | $2^{43}\cdot3^{9}\cdot5^{34}$ |
| 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, 400.2.a.a$^{2}$, 400.2.a.b$^{2}$, 400.2.a.g$^{2}$, 1200.2.a.h, 1200.2.a.j, 1200.2.a.l, 1200.2.a.q |
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.1.6 | $30$ | $2$ | $2$ | $7$ | $0$ | $1^{10}$ |
| 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.x.1.10 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.bi.1.20 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.ct.1.7 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.cu.1.8 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.ic.1.8 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{16}$ |
| 60.960.33-60.ie.1.10 | $60$ | $2$ | $2$ | $33$ | $13$ | $1^{16}$ |
| 60.960.33-60.ig.1.3 | $60$ | $2$ | $2$ | $33$ | $13$ | $1^{16}$ |
| 60.960.33-60.ii.1.8 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{16}$ |
| 60.960.33-60.nf.1.14 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{16}$ |
| 60.960.33-60.ng.1.11 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{16}$ |
| 60.960.33-60.nj.1.4 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{16}$ |
| 60.960.33-60.nk.1.8 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{16}$ |
| 60.960.33-60.no.1.13 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{16}$ |
| 60.960.33-60.np.1.12 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.ns.1.8 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.nt.1.8 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{16}$ |
| 60.960.33-60.pe.1.11 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{16}$ |
| 60.960.33-60.pf.1.9 | $60$ | $2$ | $2$ | $33$ | $11$ | $1^{16}$ |
| 60.960.33-60.pm.1.11 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{16}$ |
| 60.960.33-60.pn.1.9 | $60$ | $2$ | $2$ | $33$ | $5$ | $1^{16}$ |
| 60.960.33-60.qv.1.11 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{16}$ |
| 60.960.33-60.qx.1.10 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{16}$ |
| 60.960.33-60.ra.1.11 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.rb.1.12 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{16}$ |
| 60.1440.49-60.btn.1.7 | $60$ | $3$ | $3$ | $49$ | $8$ | $1^{32}$ |
| 60.1440.53-60.dma.1.6 | $60$ | $3$ | $3$ | $53$ | $14$ | $1^{36}$ |