Invariants
| Level: | $60$ | $\SL_2$-level: | $4$ | ||||
| Index: | $12$ | $\PSL_2$-index: | $12$ | ||||
| Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}$ | Cusp orbits | $2^{2}$ | ||
| 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: | 4E0 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.12.0.12 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}23&2\\51&11\end{bmatrix}$, $\begin{bmatrix}23&10\\27&19\end{bmatrix}$, $\begin{bmatrix}33&34\\5&51\end{bmatrix}$ |
| 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: | $184320$ |
Models
Smooth plane model Smooth plane model
| $ 0 $ | $=$ | $ x^{2} - 960 y^{2} - 15 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 |
|---|---|---|---|---|---|
| 4.6.0.d.1 | $4$ | $2$ | $2$ | $0$ | $0$ |
| 60.6.0.a.1 | $60$ | $2$ | $2$ | $0$ | $0$ |
| 60.6.0.b.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 |
|---|---|---|---|---|
| 60.36.2.fn.1 | $60$ | $3$ | $3$ | $2$ |
| 60.48.1.bt.1 | $60$ | $4$ | $4$ | $1$ |
| 60.60.4.bv.1 | $60$ | $5$ | $5$ | $4$ |
| 60.72.3.rv.1 | $60$ | $6$ | $6$ | $3$ |
| 60.120.7.fv.1 | $60$ | $10$ | $10$ | $7$ |
| 120.24.1.u.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.w.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.ij.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.ik.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.pt.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.pu.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.qi.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.qk.1 | $120$ | $2$ | $2$ | $1$ |
| 180.324.22.fr.1 | $180$ | $27$ | $27$ | $22$ |