Invariants
Level: | $60$ | $\SL_2$-level: | $5$ | ||||
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 | $1^{2}\cdot5^{2}$ | 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: | 5D0 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.12.0.24 |
Level structure
$\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}11&40\\3&59\end{bmatrix}$, $\begin{bmatrix}19&20\\36&37\end{bmatrix}$, $\begin{bmatrix}37&0\\41&7\end{bmatrix}$, $\begin{bmatrix}46&5\\49&7\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 60-isogeny field degree: | $24$ |
Cyclic 60-torsion field degree: | $384$ |
Full 60-torsion field degree: | $184320$ |
Models
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 78 x^{2} - 60 x z - y^{2} + 12 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 |
---|---|---|---|---|---|
$X_0(5)$ | $5$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
60.24.1.d.2 | $60$ | $2$ | $2$ | $1$ |
60.24.1.f.2 | $60$ | $2$ | $2$ | $1$ |
60.24.1.s.1 | $60$ | $2$ | $2$ | $1$ |
60.24.1.u.1 | $60$ | $2$ | $2$ | $1$ |
60.24.1.z.1 | $60$ | $2$ | $2$ | $1$ |
60.24.1.bb.1 | $60$ | $2$ | $2$ | $1$ |
60.24.1.bf.2 | $60$ | $2$ | $2$ | $1$ |
60.24.1.bh.2 | $60$ | $2$ | $2$ | $1$ |
60.36.0.b.2 | $60$ | $3$ | $3$ | $0$ |
60.36.2.ft.1 | $60$ | $3$ | $3$ | $2$ |
60.48.1.bx.2 | $60$ | $4$ | $4$ | $1$ |
60.48.3.cp.1 | $60$ | $4$ | $4$ | $3$ |
60.60.0.a.1 | $60$ | $5$ | $5$ | $0$ |
120.24.1.cm.1 | $120$ | $2$ | $2$ | $1$ |
120.24.1.cs.2 | $120$ | $2$ | $2$ | $1$ |
120.24.1.hd.1 | $120$ | $2$ | $2$ | $1$ |
120.24.1.hm.2 | $120$ | $2$ | $2$ | $1$ |
120.24.1.jc.1 | $120$ | $2$ | $2$ | $1$ |
120.24.1.ji.1 | $120$ | $2$ | $2$ | $1$ |
120.24.1.jx.1 | $120$ | $2$ | $2$ | $1$ |
120.24.1.kg.1 | $120$ | $2$ | $2$ | $1$ |
180.324.22.hr.1 | $180$ | $27$ | $27$ | $22$ |
300.60.0.a.2 | $300$ | $5$ | $5$ | $0$ |