Invariants
| Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $3600$ | ||
| 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 | $4^{6}\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $10$ | ||||||
| $\Q$-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: | 60.1920.65.6925 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}21&34\\14&19\end{bmatrix}$, $\begin{bmatrix}21&34\\34&9\end{bmatrix}$, $\begin{bmatrix}41&18\\18&35\end{bmatrix}$, $\begin{bmatrix}59&4\\44&21\end{bmatrix}$, $\begin{bmatrix}59&54\\48&11\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.960.65.dd.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: | $2^{148}\cdot3^{77}\cdot5^{130}$ |
| 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$^{2}$, 300.2.a.b, 300.2.e.a, 300.2.e.b, 300.2.e.c, 300.2.e.e$^{2}$, 3600.2.a.a, 3600.2.a.bb$^{2}$, 3600.2.a.bc$^{2}$, 3600.2.a.bf$^{2}$, 3600.2.a.bg, 3600.2.a.bi, 3600.2.a.bl, 3600.2.a.bm, 3600.2.a.d, 3600.2.a.j, 3600.2.a.k$^{2}$, 3600.2.a.n, 3600.2.a.o, 3600.2.a.s |
Rational points
This modular curve has no $\Q_p$ points for $p=7,43,53$, 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.2.29 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{18}\cdot4^{2}\cdot8$ |
| 60.960.31-60.c.2.18 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{18}\cdot8^{2}$ |
| 60.960.31-60.c.2.55 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{18}\cdot8^{2}$ |
| 60.960.33-60.v.1.2 | $60$ | $2$ | $2$ | $33$ | $10$ | $4^{2}\cdot8^{3}$ |
| 60.960.33-60.v.1.25 | $60$ | $2$ | $2$ | $33$ | $10$ | $4^{2}\cdot8^{3}$ |
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.u.2.11 | $60$ | $2$ | $2$ | $129$ | $19$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.x.1.15 | $60$ | $2$ | $2$ | $129$ | $20$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.y.1.14 | $60$ | $2$ | $2$ | $129$ | $20$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.bb.1.11 | $60$ | $2$ | $2$ | $129$ | $20$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.ca.1.9 | $60$ | $2$ | $2$ | $129$ | $17$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.cd.1.9 | $60$ | $2$ | $2$ | $129$ | $23$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.ce.1.13 | $60$ | $2$ | $2$ | $129$ | $20$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.ch.1.15 | $60$ | $2$ | $2$ | $129$ | $11$ | $1^{32}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.ct.1.3 | $60$ | $2$ | $2$ | $137$ | $27$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.cu.4.4 | $60$ | $2$ | $2$ | $137$ | $18$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.cz.4.7 | $60$ | $2$ | $2$ | $137$ | $24$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.da.3.5 | $60$ | $2$ | $2$ | $137$ | $20$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.fv.4.8 | $60$ | $2$ | $2$ | $137$ | $25$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.fw.1.1 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.gh.3.4 | $60$ | $2$ | $2$ | $137$ | $22$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.gi.4.4 | $60$ | $2$ | $2$ | $137$ | $19$ | $1^{36}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.3840.137-60.pl.2.8 | $60$ | $2$ | $2$ | $137$ | $25$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.pm.3.7 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.px.2.6 | $60$ | $2$ | $2$ | $137$ | $22$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.py.3.8 | $60$ | $2$ | $2$ | $137$ | $19$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.qb.2.3 | $60$ | $2$ | $2$ | $137$ | $27$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.qc.2.8 | $60$ | $2$ | $2$ | $137$ | $18$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.qh.3.6 | $60$ | $2$ | $2$ | $137$ | $24$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.qi.1.5 | $60$ | $2$ | $2$ | $137$ | $20$ | $1^{36}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.5760.193-60.hd.3.3 | $60$ | $3$ | $3$ | $193$ | $27$ | $1^{64}\cdot4^{4}\cdot8^{6}$ |
| 60.5760.209-60.de.1.17 | $60$ | $3$ | $3$ | $209$ | $33$ | $1^{70}\cdot2^{5}\cdot4^{2}\cdot8^{7}$ |