Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $2^{5}$ | ||
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: | 8O0 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}15&16\\28&31\end{bmatrix}$, $\begin{bmatrix}47&0\\48&11\end{bmatrix}$, $\begin{bmatrix}55&92\\62&117\end{bmatrix}$, $\begin{bmatrix}73&60\\4&19\end{bmatrix}$, $\begin{bmatrix}89&28\\2&93\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.0.bu.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $368640$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
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
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.48.0-8.e.1.12 | $24$ | $2$ | $2$ | $0$ | $0$ |
40.48.0-8.e.1.9 | $40$ | $2$ | $2$ | $0$ | $0$ |
120.48.0-120.t.1.9 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.t.1.21 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.x.1.15 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.x.1.33 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.192.1-120.ba.1.5 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.bf.1.7 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.cy.1.6 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.db.1.8 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.dy.1.7 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.dz.1.8 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.eg.1.5 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.eh.1.7 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.gm.1.13 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.gn.1.15 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.gu.1.9 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.gv.1.13 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.hc.1.9 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.hd.1.13 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.hk.1.11 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.hl.1.15 | $120$ | $2$ | $2$ | $1$ |
120.288.8-120.mf.2.1 | $120$ | $3$ | $3$ | $8$ |
120.384.7-120.gt.2.10 | $120$ | $4$ | $4$ | $7$ |
120.480.16-120.cj.2.26 | $120$ | $5$ | $5$ | $16$ |