Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | ||||
| Index: | $12$ | $\PSL_2$-index: | $12$ | ||||
| Genus: | $0 = 1 + \frac{ 12 }{12} - \frac{ 4 }{4} - \frac{ 0 }{3} - \frac{ 2 }{2}$ | ||||||
| Cusps: | $2$ (all of which are rational) | Cusp widths | $4\cdot8$ | Cusp orbits | $1^{2}$ | ||
| Elliptic points: | $4$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8B0 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}14&85\\21&98\end{bmatrix}$, $\begin{bmatrix}25&4\\96&83\end{bmatrix}$, $\begin{bmatrix}56&113\\15&112\end{bmatrix}$, $\begin{bmatrix}70&51\\49&10\end{bmatrix}$, $\begin{bmatrix}71&20\\112&51\end{bmatrix}$, $\begin{bmatrix}73&72\\32&59\end{bmatrix}$ |
| 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.ja.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.jb.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.jc.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.jd.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.ji.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.jj.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.jk.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.jl.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.jq.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.jr.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.js.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.jt.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.jy.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.jz.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.ka.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.kb.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.ki.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.kj.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.ko.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.kp.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.kq.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.kr.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.kw.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.kx.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.ky.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.kz.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.le.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.lf.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.lg.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.0.lh.1 | $120$ | $2$ | $2$ | $0$ |
| 120.24.1.a.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.f.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.m.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.o.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.z.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.ba.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.bd.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.be.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.dp.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.dq.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.dt.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.du.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.ef.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.eg.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.ej.1 | $120$ | $2$ | $2$ | $1$ |
| 120.24.1.ek.1 | $120$ | $2$ | $2$ | $1$ |
| 120.36.0.gk.1 | $120$ | $3$ | $3$ | $0$ |
| 120.48.3.da.1 | $120$ | $4$ | $4$ | $3$ |
| 120.60.4.hk.1 | $120$ | $5$ | $5$ | $4$ |
| 120.72.3.gqm.1 | $120$ | $6$ | $6$ | $3$ |
| 120.120.7.bnw.1 | $120$ | $10$ | $10$ | $7$ |