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 | $2^{3}$ | ||
| 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: | 60.24.0.32 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}11&32\\12&7\end{bmatrix}$, $\begin{bmatrix}35&6\\4&5\end{bmatrix}$, $\begin{bmatrix}43&46\\1&9\end{bmatrix}$ |
| 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 $ | $=$ | $ 240 x^{2} + 32 y^{2} + 8 y z - 7 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 |
|---|---|---|---|---|---|
| $X_{\mathrm{sp}}^+(4)$ | $4$ | $2$ | $2$ | $0$ | $0$ |
| 60.12.0.bj.1 | $60$ | $2$ | $2$ | $0$ | $0$ |
| 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.cx.1 | $60$ | $3$ | $3$ | $4$ |
| 60.96.3.cb.1 | $60$ | $4$ | $4$ | $3$ |
| 60.120.8.bz.1 | $60$ | $5$ | $5$ | $8$ |
| 60.144.7.mp.1 | $60$ | $6$ | $6$ | $7$ |
| 60.240.15.hh.1 | $60$ | $10$ | $10$ | $15$ |
| 120.48.1.tz.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.uj.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.xd.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.xj.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.bst.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.bsz.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.btl.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.btn.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.chl.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.chn.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.chz.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.cif.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.cnd.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.cnj.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.cqt.1 | $120$ | $2$ | $2$ | $1$ |
| 120.48.1.crd.1 | $120$ | $2$ | $2$ | $1$ |