Invariants
| Level: | $60$ | $\SL_2$-level: | $4$ | ||||
| Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $4^{6}$ | Cusp orbits | $2\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 4G0 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.24.0.114 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}13&38\\54&55\end{bmatrix}$, $\begin{bmatrix}21&52\\13&15\end{bmatrix}$, $\begin{bmatrix}55&34\\59&13\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 60-isogeny field degree: | $48$ |
| Cyclic 60-torsion field degree: | $768$ |
| Full 60-torsion field degree: | $92160$ |
Models
Smooth plane model Smooth plane model
| $ 0 $ | $=$ | $ 48 x^{2} - 5 y^{2} - 10 y z + 10 z^{2} $ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
Cover information
Click on a modular curve in the diagram to see information about it.
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This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 12.12.0.l.1 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 20.12.0.o.1 | $20$ | $2$ | $2$ | $0$ | $0$ |
| 60.12.0.bn.1 | $60$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 60.72.4.bz.1 | $60$ | $3$ | $3$ | $4$ |
| 60.96.3.bp.1 | $60$ | $4$ | $4$ | $3$ |
| 60.120.8.z.1 | $60$ | $5$ | $5$ | $8$ |
| 60.144.7.ke.1 | $60$ | $6$ | $6$ | $7$ |
| 60.240.15.dn.1 | $60$ | $10$ | $10$ | $15$ |
| 120.48.1.oz.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.pj.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.pr.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.px.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.bbb.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.bbh.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.bdp.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.bdr.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.blx.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.blz.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.boh.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.bon.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.bwb.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.bwh.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.bwp.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.bwz.1 | $120$ | $2$ | $2$ | $1$ |