Invariants
| Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $1800$ | ||
| 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: | $4$ | ||||||
| $\Q$-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: | 60.480.17.1356 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}4&45\\33&26\end{bmatrix}$, $\begin{bmatrix}13&28\\18&29\end{bmatrix}$, $\begin{bmatrix}31&18\\24&29\end{bmatrix}$, $\begin{bmatrix}56&47\\45&14\end{bmatrix}$, $\begin{bmatrix}59&22\\42&13\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.240.17.mv.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: | $2^{33}\cdot3^{25}\cdot5^{34}$ |
| 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, 1800.2.a.a, 1800.2.a.g, 1800.2.a.j$^{2}$, 1800.2.a.q, 1800.2.a.r$^{2}$, 1800.2.a.s$^{2}$, 1800.2.a.t |
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 |
|---|---|---|---|---|---|---|
| 60.240.7-30.h.1.14 | $60$ | $2$ | $2$ | $7$ | $0$ | $1^{10}$ |
| 60.240.7-30.h.1.26 | $60$ | $2$ | $2$ | $7$ | $0$ | $1^{10}$ |
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.y.1.6 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.bo.1.17 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.cw.1.6 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.cz.1.4 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.ki.1.4 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{16}$ |
| 60.960.33-60.kl.1.10 | $60$ | $2$ | $2$ | $33$ | $17$ | $1^{16}$ |
| 60.960.33-60.km.1.2 | $60$ | $2$ | $2$ | $33$ | $17$ | $1^{16}$ |
| 60.960.33-60.kp.1.8 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{16}$ |
| 60.960.33-60.lz.1.14 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.mb.1.12 | $60$ | $2$ | $2$ | $33$ | $11$ | $1^{16}$ |
| 60.960.33-60.md.1.4 | $60$ | $2$ | $2$ | $33$ | $11$ | $1^{16}$ |
| 60.960.33-60.mf.1.7 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.mp.1.14 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.mr.1.11 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{16}$ |
| 60.960.33-60.mt.1.8 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{16}$ |
| 60.960.33-60.mv.1.4 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.pi.1.16 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{16}$ |
| 60.960.33-60.pk.1.13 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{16}$ |
| 60.960.33-60.py.1.14 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.qa.1.9 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{16}$ |
| 60.960.33-60.qb.1.13 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{16}$ |
| 60.960.33-60.qe.1.12 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{16}$ |
| 60.960.33-60.qn.1.11 | $60$ | $2$ | $2$ | $33$ | $9$ | $1^{16}$ |
| 60.960.33-60.qq.1.24 | $60$ | $2$ | $2$ | $33$ | $9$ | $1^{16}$ |
| 60.1440.49-60.btq.1.3 | $60$ | $3$ | $3$ | $49$ | $12$ | $1^{32}$ |
| 60.1440.53-60.dyq.1.6 | $60$ | $3$ | $3$ | $53$ | $15$ | $1^{36}$ |