Invariants
| Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $3600$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $15 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $10^{6}\cdot30^{6}$ | Cusp orbits | $2^{2}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $1$ | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 10$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 10$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 30A15 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.480.15.2071 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}8&57\\27&2\end{bmatrix}$, $\begin{bmatrix}16&47\\45&14\end{bmatrix}$, $\begin{bmatrix}29&2\\12&23\end{bmatrix}$, $\begin{bmatrix}29&36\\36&1\end{bmatrix}$, $\begin{bmatrix}50&23\\27&20\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.240.15.fd.1 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $12$ |
| Cyclic 60-torsion field degree: | $96$ |
| Full 60-torsion field degree: | $4608$ |
Jacobian
| Conductor: | $2^{35}\cdot3^{21}\cdot5^{26}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{15}$ |
| Newforms: | 50.2.a.b$^{2}$, 75.2.a.a$^{2}$, 75.2.a.b$^{2}$, 150.2.a.b, 720.2.a.c, 720.2.a.h$^{2}$, 720.2.a.j, 3600.2.a.bk, 3600.2.a.l$^{2}$, 3600.2.a.z |
Rational points
This modular curve has no $\Q_p$ points for $p=53$, 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 |
|---|---|---|---|---|---|---|
| 60.48.0-60.r.1.6 | $60$ | $10$ | $10$ | $0$ | $0$ | full Jacobian |
| 60.240.7-30.h.1.14 | $60$ | $2$ | $2$ | $7$ | $0$ | $1^{8}$ |
| 60.240.7-30.h.1.15 | $60$ | $2$ | $2$ | $7$ | $0$ | $1^{8}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 60.960.29-60.nh.1.10 | $60$ | $2$ | $2$ | $29$ | $5$ | $1^{14}$ |
| 60.960.29-60.ni.1.11 | $60$ | $2$ | $2$ | $29$ | $6$ | $1^{14}$ |
| 60.960.29-60.no.1.15 | $60$ | $2$ | $2$ | $29$ | $7$ | $1^{14}$ |
| 60.960.29-60.np.1.14 | $60$ | $2$ | $2$ | $29$ | $2$ | $1^{14}$ |
| 60.960.29-60.os.1.4 | $60$ | $2$ | $2$ | $29$ | $1$ | $1^{14}$ |
| 60.960.29-60.ot.1.10 | $60$ | $2$ | $2$ | $29$ | $4$ | $1^{14}$ |
| 60.960.29-60.oz.1.14 | $60$ | $2$ | $2$ | $29$ | $7$ | $1^{14}$ |
| 60.960.29-60.pa.1.15 | $60$ | $2$ | $2$ | $29$ | $6$ | $1^{14}$ |
| 60.960.33-60.cl.1.12 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{18}$ |
| 60.960.33-60.cn.1.14 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{18}$ |
| 60.960.33-60.li.1.11 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{18}$ |
| 60.960.33-60.ll.1.9 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{18}$ |
| 60.960.33-60.mi.1.10 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{18}$ |
| 60.960.33-60.mj.1.12 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{18}$ |
| 60.960.33-60.mq.1.10 | $60$ | $2$ | $2$ | $33$ | $12$ | $1^{18}$ |
| 60.960.33-60.mr.1.11 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{18}$ |
| 60.960.33-60.np.1.12 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{18}$ |
| 60.960.33-60.nq.1.9 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{18}$ |
| 60.960.33-60.nx.1.12 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{18}$ |
| 60.960.33-60.ny.1.10 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{18}$ |
| 60.960.33-60.oj.1.13 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{18}$ |
| 60.960.33-60.om.1.15 | $60$ | $2$ | $2$ | $33$ | $1$ | $1^{18}$ |
| 60.960.33-60.os.1.14 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{18}$ |
| 60.960.33-60.ou.1.23 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{18}$ |
| 60.1440.43-60.ox.1.13 | $60$ | $3$ | $3$ | $43$ | $6$ | $1^{28}$ |
| 60.1440.49-60.bki.1.9 | $60$ | $3$ | $3$ | $49$ | $10$ | $1^{34}$ |