Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot4$ | ||
| Elliptic points: | $0$ 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: | 8G0 |
Level structure
| $\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}3&20\\64&7\end{bmatrix}$, $\begin{bmatrix}23&102\\88&49\end{bmatrix}$, $\begin{bmatrix}27&16\\14&103\end{bmatrix}$, $\begin{bmatrix}51&40\\70&83\end{bmatrix}$, $\begin{bmatrix}61&28\\12&13\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 120.24.0.v.1 for the level structure with $-I$) |
| Cyclic 120-isogeny field degree: | $96$ |
| Cyclic 120-torsion field degree: | $3072$ |
| Full 120-torsion field degree: | $737280$ |
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 |
|---|---|---|---|---|---|
| 24.24.0-4.a.1.1 | $24$ | $2$ | $2$ | $0$ | $0$ |
| 40.24.0-4.a.1.3 | $40$ | $2$ | $2$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 120.96.1-120.a.1.5 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.c.1.5 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.f.1.7 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.g.1.7 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.i.1.7 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.k.1.7 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.n.1.11 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.t.1.5 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.bd.1.2 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.be.1.1 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.bh.1.3 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.bi.1.4 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.bl.1.3 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.bm.1.8 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.bp.1.5 | $120$ | $2$ | $2$ | $1$ |
| 120.96.1-120.bq.1.1 | $120$ | $2$ | $2$ | $1$ |
| 120.144.4-120.em.1.9 | $120$ | $3$ | $3$ | $4$ |
| 120.192.3-120.fw.1.14 | $120$ | $4$ | $4$ | $3$ |
| 120.240.8-120.be.1.12 | $120$ | $5$ | $5$ | $8$ |
| 120.288.7-120.bdz.1.3 | $120$ | $6$ | $6$ | $7$ |
| 120.480.15-120.em.1.8 | $120$ | $10$ | $10$ | $15$ |