Invariants
| Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $600$ | ||
| Index: | $1920$ | $\PSL_2$-index: | $960$ | ||||
| Genus: | $65 = 1 + \frac{ 960 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 32 }{2}$ | ||||||
| Cusps: | $32$ (none of which are rational) | Cusp widths | $10^{8}\cdot20^{8}\cdot30^{8}\cdot60^{8}$ | Cusp orbits | $2^{4}\cdot4^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $1$ | ||||||
| $\Q$-gonality: | $10 \le \gamma \le 20$ | ||||||
| $\overline{\Q}$-gonality: | $10 \le \gamma \le 20$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.1920.65.1046 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}1&32\\0&59\end{bmatrix}$, $\begin{bmatrix}13&20\\30&13\end{bmatrix}$, $\begin{bmatrix}25&52\\12&59\end{bmatrix}$, $\begin{bmatrix}47&46\\48&13\end{bmatrix}$, $\begin{bmatrix}55&52\\12&49\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.960.65.j.1 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $6$ |
| Cyclic 60-torsion field degree: | $48$ |
| Full 60-torsion field degree: | $1152$ |
Jacobian
| Conductor: | $2^{115}\cdot3^{51}\cdot5^{112}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{33}\cdot8^{4}$ |
| Newforms: | 15.2.a.a, 20.2.a.a$^{2}$, 24.2.a.a, 30.2.a.a, 40.2.a.a$^{2}$, 50.2.a.a$^{2}$, 50.2.a.b$^{4}$, 60.2.e.a, 75.2.a.a$^{3}$, 75.2.a.b$^{3}$, 75.2.a.c, 100.2.a.a$^{2}$, 120.2.a.a, 120.2.a.b, 150.2.a.b$^{2}$, 200.2.a.a$^{2}$, 300.2.a.b, 300.2.a.c, 300.2.e.c, 300.2.e.d, 300.2.e.e, 600.2.a.f, 600.2.a.h, 600.2.a.i |
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 |
|---|---|---|---|---|---|---|
| 60.192.1-60.f.4.3 | $60$ | $10$ | $10$ | $1$ | $0$ | $1^{32}\cdot8^{4}$ |
| 60.960.31-60.a.2.7 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{18}\cdot8^{2}$ |
| 60.960.31-60.a.2.51 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{18}\cdot8^{2}$ |
| 60.960.31-60.b.2.18 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{18}\cdot8^{2}$ |
| 60.960.31-60.b.2.51 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{18}\cdot8^{2}$ |
| 60.960.33-60.r.1.2 | $60$ | $2$ | $2$ | $33$ | $1$ | $8^{4}$ |
| 60.960.33-60.r.1.32 | $60$ | $2$ | $2$ | $33$ | $1$ | $8^{4}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 60.3840.129-60.bx.2.7 | $60$ | $2$ | $2$ | $129$ | $6$ | $1^{32}\cdot4^{4}\cdot8^{2}$ |
| 60.3840.129-60.bz.2.7 | $60$ | $2$ | $2$ | $129$ | $15$ | $1^{32}\cdot4^{4}\cdot8^{2}$ |
| 60.3840.129-60.cf.1.5 | $60$ | $2$ | $2$ | $129$ | $12$ | $1^{32}\cdot4^{4}\cdot8^{2}$ |
| 60.3840.129-60.ch.2.5 | $60$ | $2$ | $2$ | $129$ | $11$ | $1^{32}\cdot4^{4}\cdot8^{2}$ |
| 60.3840.129-60.dd.1.7 | $60$ | $2$ | $2$ | $129$ | $6$ | $1^{32}\cdot4^{4}\cdot8^{2}$ |
| 60.3840.129-60.df.2.5 | $60$ | $2$ | $2$ | $129$ | $11$ | $1^{32}\cdot4^{4}\cdot8^{2}$ |
| 60.3840.129-60.dl.1.7 | $60$ | $2$ | $2$ | $129$ | $10$ | $1^{32}\cdot4^{4}\cdot8^{2}$ |
| 60.3840.129-60.dn.4.1 | $60$ | $2$ | $2$ | $129$ | $19$ | $1^{32}\cdot4^{4}\cdot8^{2}$ |
| 60.3840.137-60.cj.2.8 | $60$ | $2$ | $2$ | $137$ | $9$ | $1^{36}\cdot2^{6}\cdot4^{2}\cdot8^{2}$ |
| 60.3840.137-60.ck.3.4 | $60$ | $2$ | $2$ | $137$ | $8$ | $1^{36}\cdot2^{6}\cdot4^{2}\cdot8^{2}$ |
| 60.3840.137-60.cp.3.4 | $60$ | $2$ | $2$ | $137$ | $14$ | $1^{36}\cdot2^{6}\cdot4^{2}\cdot8^{2}$ |
| 60.3840.137-60.cr.2.9 | $60$ | $2$ | $2$ | $137$ | $13$ | $1^{36}\cdot2^{6}\cdot4^{2}\cdot8^{2}$ |
| 60.3840.137-60.fw.1.1 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot2^{4}\cdot4^{5}\cdot8$ |
| 60.3840.137-60.fx.1.2 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot2^{4}\cdot4^{5}\cdot8$ |
| 60.3840.137-60.ga.1.2 | $60$ | $2$ | $2$ | $137$ | $11$ | $1^{36}\cdot2^{4}\cdot4^{5}\cdot8$ |
| 60.3840.137-60.gb.1.2 | $60$ | $2$ | $2$ | $137$ | $11$ | $1^{36}\cdot2^{4}\cdot4^{5}\cdot8$ |
| 60.3840.137-60.iu.1.2 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot2^{4}\cdot4^{5}\cdot8$ |
| 60.3840.137-60.iv.1.2 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot2^{4}\cdot4^{5}\cdot8$ |
| 60.3840.137-60.iy.1.2 | $60$ | $2$ | $2$ | $137$ | $11$ | $1^{36}\cdot2^{4}\cdot4^{5}\cdot8$ |
| 60.3840.137-60.iz.1.1 | $60$ | $2$ | $2$ | $137$ | $11$ | $1^{36}\cdot2^{4}\cdot4^{5}\cdot8$ |
| 60.3840.137-60.jj.1.4 | $60$ | $2$ | $2$ | $137$ | $9$ | $1^{36}\cdot2^{6}\cdot4^{2}\cdot8^{2}$ |
| 60.3840.137-60.jk.1.2 | $60$ | $2$ | $2$ | $137$ | $8$ | $1^{36}\cdot2^{6}\cdot4^{2}\cdot8^{2}$ |
| 60.3840.137-60.jp.1.2 | $60$ | $2$ | $2$ | $137$ | $14$ | $1^{36}\cdot2^{6}\cdot4^{2}\cdot8^{2}$ |
| 60.3840.137-60.jr.4.3 | $60$ | $2$ | $2$ | $137$ | $13$ | $1^{36}\cdot2^{6}\cdot4^{2}\cdot8^{2}$ |
| 60.5760.193-60.fe.1.9 | $60$ | $3$ | $3$ | $193$ | $7$ | $1^{64}\cdot4^{4}\cdot8^{6}$ |
| 60.5760.209-60.cx.1.3 | $60$ | $3$ | $3$ | $209$ | $15$ | $1^{72}\cdot2^{4}\cdot8^{8}$ |