Invariants
| Level: | $60$ | $\SL_2$-level: | $20$ | Newform level: | $1800$ | ||
| Index: | $720$ | $\PSL_2$-index: | $360$ | ||||
| Genus: | $19 = 1 + \frac{ 360 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (of which $4$ are rational) | Cusp widths | $10^{12}\cdot20^{12}$ | Cusp orbits | $1^{4}\cdot2^{2}\cdot4^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $4$ | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 6$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 6$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20A19 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.720.19.12 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}1&0\\20&17\end{bmatrix}$, $\begin{bmatrix}1&10\\30&29\end{bmatrix}$, $\begin{bmatrix}31&40\\40&57\end{bmatrix}$, $\begin{bmatrix}39&25\\50&29\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.360.19.px.1 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $8$ |
| Cyclic 60-torsion field degree: | $64$ |
| Full 60-torsion field degree: | $3072$ |
Jacobian
| Conductor: | $2^{49}\cdot3^{30}\cdot5^{33}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{9}\cdot2^{5}$ |
| Newforms: | 50.2.a.a, 50.2.a.b, 50.2.b.a, 360.2.a.a, 360.2.f.c$^{2}$, 1800.2.a.h, 1800.2.a.j, 1800.2.a.r, 1800.2.a.s, 1800.2.a.v$^{2}$, 1800.2.f.a, 1800.2.f.f |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 10.360.4-10.a.1.3 | $10$ | $2$ | $2$ | $4$ | $0$ | $1^{7}\cdot2^{4}$ |
| 60.144.3-60.xu.1.7 | $60$ | $5$ | $5$ | $3$ | $0$ | $1^{8}\cdot2^{4}$ |
| 60.144.3-60.xu.2.15 | $60$ | $5$ | $5$ | $3$ | $0$ | $1^{8}\cdot2^{4}$ |
| 60.360.4-10.a.1.6 | $60$ | $2$ | $2$ | $4$ | $0$ | $1^{7}\cdot2^{4}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 60.1440.37-60.m.1.12 | $60$ | $2$ | $2$ | $37$ | $6$ | $1^{10}\cdot2^{4}$ |
| 60.1440.37-60.co.1.2 | $60$ | $2$ | $2$ | $37$ | $8$ | $1^{10}\cdot2^{4}$ |
| 60.1440.37-60.ey.1.2 | $60$ | $2$ | $2$ | $37$ | $8$ | $1^{10}\cdot2^{4}$ |
| 60.1440.37-60.fd.1.4 | $60$ | $2$ | $2$ | $37$ | $6$ | $1^{10}\cdot2^{4}$ |
| 60.1440.37-60.id.1.4 | $60$ | $2$ | $2$ | $37$ | $5$ | $1^{10}\cdot2^{4}$ |
| 60.1440.37-60.ii.1.1 | $60$ | $2$ | $2$ | $37$ | $7$ | $1^{10}\cdot2^{4}$ |
| 60.1440.37-60.it.1.1 | $60$ | $2$ | $2$ | $37$ | $7$ | $1^{10}\cdot2^{4}$ |
| 60.1440.37-60.jd.1.1 | $60$ | $2$ | $2$ | $37$ | $5$ | $1^{10}\cdot2^{4}$ |
| 60.2160.79-60.emf.1.16 | $60$ | $3$ | $3$ | $79$ | $13$ | $1^{24}\cdot2^{18}$ |
| 60.2880.97-60.bql.1.9 | $60$ | $4$ | $4$ | $97$ | $16$ | $1^{40}\cdot2^{19}$ |