Invariants
| Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $900$ | ||
| 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 | $5^{4}\cdot15^{4}\cdot20^{2}\cdot60^{2}$ | 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: | 60V15 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.480.15.2074 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}4&5\\33&16\end{bmatrix}$, $\begin{bmatrix}11&0\\0&1\end{bmatrix}$, $\begin{bmatrix}23&38\\48&59\end{bmatrix}$, $\begin{bmatrix}26&27\\45&44\end{bmatrix}$, $\begin{bmatrix}43&6\\30&7\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.240.15.ff.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: | $2^{12}\cdot3^{21}\cdot5^{26}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{15}$ |
| Newforms: | 45.2.a.a, 50.2.a.b$^{2}$, 75.2.a.a$^{2}$, 75.2.a.b$^{2}$, 90.2.a.c, 150.2.a.b, 180.2.a.a$^{2}$, 225.2.a.a, 450.2.a.g$^{2}$, 900.2.a.c |
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.t.1.8 | $60$ | $10$ | $10$ | $0$ | $0$ | full Jacobian |
| 60.240.7-30.h.1.14 | $60$ | $2$ | $2$ | $7$ | $0$ | $1^{8}$ |
| 60.240.7-30.h.1.27 | $60$ | $2$ | $2$ | $7$ | $0$ | $1^{8}$ |
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.nl.1.5 | $60$ | $2$ | $2$ | $29$ | $3$ | $1^{14}$ |
| 60.960.29-60.nm.1.2 | $60$ | $2$ | $2$ | $29$ | $8$ | $1^{14}$ |
| 60.960.29-60.ns.1.7 | $60$ | $2$ | $2$ | $29$ | $5$ | $1^{14}$ |
| 60.960.29-60.nt.1.6 | $60$ | $2$ | $2$ | $29$ | $4$ | $1^{14}$ |
| 60.960.29-60.ow.1.1 | $60$ | $2$ | $2$ | $29$ | $3$ | $1^{14}$ |
| 60.960.29-60.ox.1.7 | $60$ | $2$ | $2$ | $29$ | $2$ | $1^{14}$ |
| 60.960.29-60.pd.1.5 | $60$ | $2$ | $2$ | $29$ | $3$ | $1^{14}$ |
| 60.960.29-60.pe.1.3 | $60$ | $2$ | $2$ | $29$ | $10$ | $1^{14}$ |
| 60.960.33-60.t.1.34 | $60$ | $2$ | $2$ | $33$ | $5$ | $1^{18}$ |
| 60.960.33-60.bq.1.17 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{18}$ |
| 60.960.33-60.le.1.12 | $60$ | $2$ | $2$ | $33$ | $5$ | $1^{18}$ |
| 60.960.33-60.lh.1.9 | $60$ | $2$ | $2$ | $33$ | $11$ | $1^{18}$ |
| 60.960.33-60.mm.1.1 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{18}$ |
| 60.960.33-60.mn.1.7 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{18}$ |
| 60.960.33-60.mu.1.6 | $60$ | $2$ | $2$ | $33$ | $14$ | $1^{18}$ |
| 60.960.33-60.mv.1.4 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{18}$ |
| 60.960.33-60.nt.1.8 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{18}$ |
| 60.960.33-60.nu.1.3 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{18}$ |
| 60.960.33-60.ob.1.3 | $60$ | $2$ | $2$ | $33$ | $12$ | $1^{18}$ |
| 60.960.33-60.oc.1.2 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{18}$ |
| 60.960.33-60.of.1.12 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{18}$ |
| 60.960.33-60.oi.1.15 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{18}$ |
| 60.960.33-60.or.1.11 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{18}$ |
| 60.960.33-60.ou.1.23 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{18}$ |
| 60.1440.43-60.pb.1.9 | $60$ | $3$ | $3$ | $43$ | $5$ | $1^{28}$ |
| 60.1440.49-60.bke.1.14 | $60$ | $3$ | $3$ | $49$ | $6$ | $1^{34}$ |