Invariants
| Level: | $60$ | $\SL_2$-level: | $20$ | Newform level: | $180$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $1^{4}\cdot4^{2}\cdot5^{4}\cdot20^{2}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $0$ | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20H1 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.144.1.416 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}1&55\\4&41\end{bmatrix}$, $\begin{bmatrix}11&35\\44&43\end{bmatrix}$, $\begin{bmatrix}49&0\\44&7\end{bmatrix}$, $\begin{bmatrix}51&5\\14&49\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.72.1.ba.1 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $8$ |
| Cyclic 60-torsion field degree: | $128$ |
| Full 60-torsion field degree: | $15360$ |
Jacobian
| Conductor: | $2^{2}\cdot3^{2}\cdot5$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 180.2.a.a |
Rational points
This modular curve has 2 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 |
|---|---|---|---|---|---|---|
| 20.72.0-10.a.1.10 | $20$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 60.72.0-10.a.1.10 | $60$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 60.288.5-60.z.2.5 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 60.288.5-60.dd.2.5 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{2}\cdot2$ |
| 60.288.5-60.ii.2.4 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{2}\cdot2$ |
| 60.288.5-60.im.2.6 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{2}\cdot2$ |
| 60.288.5-60.kt.2.6 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 60.288.5-60.kv.2.4 | $60$ | $2$ | $2$ | $5$ | $2$ | $1^{2}\cdot2$ |
| 60.288.5-60.kx.2.5 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{2}\cdot2$ |
| 60.288.5-60.ld.2.3 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{2}\cdot2$ |
| 60.432.13-60.cx.1.11 | $60$ | $3$ | $3$ | $13$ | $0$ | $1^{6}\cdot2^{3}$ |
| 60.576.13-60.jz.1.10 | $60$ | $4$ | $4$ | $13$ | $0$ | $1^{6}\cdot2^{3}$ |
| 60.720.13-60.t.1.6 | $60$ | $5$ | $5$ | $13$ | $1$ | $1^{6}\cdot2^{3}$ |
| 120.288.5-120.gw.2.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.vy.2.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cns.2.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cor.2.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.dee.2.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.des.2.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.dfi.2.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.dgy.2.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |