Invariants
| Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $1800$ | ||
| 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 | $2^{2}\cdot4^{3}\cdot8^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $6$ | ||||||
| $\Q$-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: | 60.1920.65.6916 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}1&20\\30&11\end{bmatrix}$, $\begin{bmatrix}11&54\\54&53\end{bmatrix}$, $\begin{bmatrix}21&10\\10&21\end{bmatrix}$, $\begin{bmatrix}25&6\\36&13\end{bmatrix}$, $\begin{bmatrix}39&20\\32&51\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.960.65.dc.2 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $12$ |
| Cyclic 60-torsion field degree: | $96$ |
| Full 60-torsion field degree: | $1152$ |
Jacobian
| Conductor: | $2^{116}\cdot3^{77}\cdot5^{130}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{33}\cdot4^{2}\cdot8^{3}$ |
| Newforms: | 50.2.a.b$^{4}$, 75.2.a.a$^{3}$, 75.2.a.b$^{3}$, 100.2.a.a$^{2}$, 150.2.a.b$^{2}$, 225.2.a.e, 300.2.a.b, 300.2.e.a, 300.2.e.b, 300.2.e.c, 300.2.e.e$^{2}$, 450.2.a.b, 450.2.a.c$^{2}$, 450.2.a.f, 900.2.a.a, 900.2.a.e, 900.2.a.h, 1800.2.a.e, 1800.2.a.g, 1800.2.a.h$^{2}$, 1800.2.a.j$^{2}$, 1800.2.a.q, 1800.2.a.s$^{2}$, 1800.2.a.x |
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 |
|---|---|---|---|---|---|---|
| 60.960.31-60.a.2.7 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{18}\cdot4^{2}\cdot8$ |
| 60.960.31-60.a.2.14 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{18}\cdot4^{2}\cdot8$ |
| 60.960.31-60.c.2.2 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{18}\cdot8^{2}$ |
| 60.960.31-60.c.2.37 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{18}\cdot8^{2}$ |
| 60.960.33-60.u.1.9 | $60$ | $2$ | $2$ | $33$ | $6$ | $4^{2}\cdot8^{3}$ |
| 60.960.33-60.u.1.28 | $60$ | $2$ | $2$ | $33$ | $6$ | $4^{2}\cdot8^{3}$ |
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.v.1.1 | $60$ | $2$ | $2$ | $129$ | $13$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.w.2.1 | $60$ | $2$ | $2$ | $129$ | $18$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.z.1.2 | $60$ | $2$ | $2$ | $129$ | $11$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.ba.1.3 | $60$ | $2$ | $2$ | $129$ | $21$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.cb.1.3 | $60$ | $2$ | $2$ | $129$ | $12$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.cc.1.3 | $60$ | $2$ | $2$ | $129$ | $20$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.cf.1.5 | $60$ | $2$ | $2$ | $129$ | $12$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.cg.3.3 | $60$ | $2$ | $2$ | $129$ | $11$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.cs.1.13 | $60$ | $2$ | $2$ | $137$ | $19$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.cu.1.13 | $60$ | $2$ | $2$ | $137$ | $18$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.cy.3.14 | $60$ | $2$ | $2$ | $137$ | $18$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.db.2.13 | $60$ | $2$ | $2$ | $137$ | $18$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.fu.1.13 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.fx.3.13 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.gg.3.13 | $60$ | $2$ | $2$ | $137$ | $16$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.gj.3.10 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.pk.2.8 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.pn.3.4 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.pw.1.6 | $60$ | $2$ | $2$ | $137$ | $16$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.pz.4.8 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.qa.2.4 | $60$ | $2$ | $2$ | $137$ | $19$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.qc.2.8 | $60$ | $2$ | $2$ | $137$ | $18$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.qg.4.8 | $60$ | $2$ | $2$ | $137$ | $18$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.qj.1.6 | $60$ | $2$ | $2$ | $137$ | $18$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.5760.193-60.hc.2.11 | $60$ | $3$ | $3$ | $193$ | $19$ | $1^{64}\cdot4^{4}\cdot8^{6}$ |
| 60.5760.209-60.df.1.8 | $60$ | $3$ | $3$ | $209$ | $25$ | $1^{70}\cdot2^{5}\cdot4^{2}\cdot8^{7}$ |