Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | ||||
Index: | $12$ | $\PSL_2$-index: | $6$ | ||||
Genus: | $0 = 1 + \frac{ 6 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 3 }{2}$ | ||||||
Cusps: | $3$ (all of which are rational) | Cusp widths | $1^{2}\cdot4$ | Cusp orbits | $1^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $3$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 4B0 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}23&24\\30&41\end{bmatrix}$, $\begin{bmatrix}32&43\\7&0\end{bmatrix}$, $\begin{bmatrix}36&5\\113&28\end{bmatrix}$, $\begin{bmatrix}88&27\\35&28\end{bmatrix}$, $\begin{bmatrix}88&87\\113&14\end{bmatrix}$, $\begin{bmatrix}108&95\\11&96\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 4.6.0.c.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $2949120$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points, including 95098 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map of degree 6 to the modular curve $X(1)$ :
$\displaystyle j$ | $=$ | $\displaystyle \frac{x^{6}(48x^{2}-y^{2})^{3}}{x^{10}(8x-y)(8x+y)}$ |
Modular covers
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.24.0-4.b.1.4 | $120$ | $2$ | $2$ | $0$ |
120.24.0-4.d.1.2 | $120$ | $2$ | $2$ | $0$ |
120.24.0-8.d.1.4 | $120$ | $2$ | $2$ | $0$ |
120.24.0-12.g.1.6 | $120$ | $2$ | $2$ | $0$ |
120.24.0-20.g.1.3 | $120$ | $2$ | $2$ | $0$ |
120.24.0-60.g.1.7 | $120$ | $2$ | $2$ | $0$ |
120.24.0-12.h.1.6 | $120$ | $2$ | $2$ | $0$ |
120.24.0-20.h.1.3 | $120$ | $2$ | $2$ | $0$ |
120.24.0-60.h.1.6 | $120$ | $2$ | $2$ | $0$ |
120.24.0-8.k.1.4 | $120$ | $2$ | $2$ | $0$ |
120.24.0-8.m.1.3 | $120$ | $2$ | $2$ | $0$ |
120.24.0-8.m.1.4 | $120$ | $2$ | $2$ | $0$ |
120.24.0-8.n.1.1 | $120$ | $2$ | $2$ | $0$ |
120.24.0-8.n.1.2 | $120$ | $2$ | $2$ | $0$ |
120.24.0-8.o.1.1 | $120$ | $2$ | $2$ | $0$ |
120.24.0-8.o.1.2 | $120$ | $2$ | $2$ | $0$ |
120.24.0-8.p.1.3 | $120$ | $2$ | $2$ | $0$ |
120.24.0-8.p.1.4 | $120$ | $2$ | $2$ | $0$ |
120.24.0-24.s.1.7 | $120$ | $2$ | $2$ | $0$ |
120.24.0-40.s.1.7 | $120$ | $2$ | $2$ | $0$ |
120.24.0-120.s.1.14 | $120$ | $2$ | $2$ | $0$ |
120.24.0-24.v.1.7 | $120$ | $2$ | $2$ | $0$ |
120.24.0-40.v.1.7 | $120$ | $2$ | $2$ | $0$ |
120.24.0-120.v.1.14 | $120$ | $2$ | $2$ | $0$ |
120.24.0-24.y.1.3 | $120$ | $2$ | $2$ | $0$ |
120.24.0-24.y.1.4 | $120$ | $2$ | $2$ | $0$ |
120.24.0-40.y.1.5 | $120$ | $2$ | $2$ | $0$ |
120.24.0-40.y.1.7 | $120$ | $2$ | $2$ | $0$ |
120.24.0-120.y.1.4 | $120$ | $2$ | $2$ | $0$ |
120.24.0-120.y.1.20 | $120$ | $2$ | $2$ | $0$ |
120.24.0-24.z.1.3 | $120$ | $2$ | $2$ | $0$ |
120.24.0-24.z.1.4 | $120$ | $2$ | $2$ | $0$ |
120.24.0-40.z.1.5 | $120$ | $2$ | $2$ | $0$ |
120.24.0-40.z.1.6 | $120$ | $2$ | $2$ | $0$ |
120.24.0-120.z.1.4 | $120$ | $2$ | $2$ | $0$ |
120.24.0-120.z.1.20 | $120$ | $2$ | $2$ | $0$ |
120.24.0-24.ba.1.3 | $120$ | $2$ | $2$ | $0$ |
120.24.0-24.ba.1.4 | $120$ | $2$ | $2$ | $0$ |
120.24.0-40.ba.1.5 | $120$ | $2$ | $2$ | $0$ |
120.24.0-40.ba.1.6 | $120$ | $2$ | $2$ | $0$ |
120.24.0-120.ba.1.4 | $120$ | $2$ | $2$ | $0$ |
120.24.0-120.ba.1.20 | $120$ | $2$ | $2$ | $0$ |
120.24.0-24.bb.1.3 | $120$ | $2$ | $2$ | $0$ |
120.24.0-24.bb.1.4 | $120$ | $2$ | $2$ | $0$ |
120.24.0-40.bb.1.5 | $120$ | $2$ | $2$ | $0$ |
120.24.0-40.bb.1.7 | $120$ | $2$ | $2$ | $0$ |
120.24.0-120.bb.1.4 | $120$ | $2$ | $2$ | $0$ |
120.24.0-120.bb.1.20 | $120$ | $2$ | $2$ | $0$ |
120.36.1-12.c.1.12 | $120$ | $3$ | $3$ | $1$ |
120.48.0-12.g.1.28 | $120$ | $4$ | $4$ | $0$ |
120.60.2-20.c.1.11 | $120$ | $5$ | $5$ | $2$ |
120.72.1-20.c.1.23 | $120$ | $6$ | $6$ | $1$ |
120.120.3-20.c.1.14 | $120$ | $10$ | $10$ | $3$ |