Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | ||||
| Index: | $12$ | $\PSL_2$-index: | $12$ | ||||
| Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 2 }{4} - \frac{ 0 }{3} - \frac{ 3 }{2}$ | ||||||
| Cusps: | $3$ (of which $1$ is rational) | Cusp widths | $2^{2}\cdot8$ | Cusp orbits | $1\cdot2$ | ||
| Elliptic points: | $2$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $1$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8D0 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}18&11\\53&58\end{bmatrix}$, $\begin{bmatrix}23&84\\52&43\end{bmatrix}$, $\begin{bmatrix}49&86\\70&27\end{bmatrix}$, $\begin{bmatrix}57&76\\44&71\end{bmatrix}$, $\begin{bmatrix}65&92\\4&117\end{bmatrix}$, $\begin{bmatrix}69&88\\92&37\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 120-isogeny field degree: | $96$ |
| Cyclic 120-torsion field degree: | $3072$ |
| 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 but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 4.6.0.e.1 | $4$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.24.0.w.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.bb.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.bq.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.bt.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.el.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.em.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.fi.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.fl.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.fv.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.fw.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.gs.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.gv.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.gx.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.gy.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.iw.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.iz.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.kg.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.kh.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.kk.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.kl.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.mc.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.md.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.mg.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.mh.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.ni.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.nj.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.nm.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.nn.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.oi.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.oj.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.om.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.on.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.1.bo.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.bp.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.bs.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.bt.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.gm.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.gn.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.gq.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.gr.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.ky.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.kz.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.lc.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.ld.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.mu.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.mv.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.my.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.mz.1 | $120$ | $2$ | $2$ | $1$ |
| 120.36.1.se.1 | $120$ | $3$ | $3$ | $1$ |
| 120.48.2.r.1 | $120$ | $4$ | $4$ | $2$ |
| 120.60.4.gu.1 | $120$ | $5$ | $5$ | $4$ |
| 120.72.3.fze.1 | $120$ | $6$ | $6$ | $3$ |
| 120.120.7.bfw.1 | $120$ | $10$ | $10$ | $7$ |