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 | $4^{8}\cdot8^{2}$ | Cusp orbits | $2^{3}\cdot4$ | ||
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: | 8N0 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}25&56\\92&83\end{bmatrix}$, $\begin{bmatrix}59&52\\36&67\end{bmatrix}$, $\begin{bmatrix}67&88\\48&35\end{bmatrix}$, $\begin{bmatrix}89&114\\92&29\end{bmatrix}$, $\begin{bmatrix}115&38\\32&33\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.0.t.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $768$ |
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 |
---|---|---|---|---|---|
24.48.0-24.i.2.2 | $24$ | $2$ | $2$ | $0$ | $0$ |
40.48.0-20.c.1.13 | $40$ | $2$ | $2$ | $0$ | $0$ |
60.48.0-20.c.1.1 | $60$ | $2$ | $2$ | $0$ | $0$ |
120.48.0-24.i.2.30 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.t.1.11 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.48.0-120.t.1.37 | $120$ | $2$ | $2$ | $0$ | $?$ |
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.bd.1.11 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.cu.2.5 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.dm.2.1 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.dq.1.10 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.fv.1.9 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.gf.2.11 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ha.2.3 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.hk.1.9 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.mc.2.2 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.mm.1.9 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ni.1.9 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ns.2.10 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.om.2.1 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.oq.1.11 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ot.1.13 | $120$ | $2$ | $2$ | $1$ |
120.192.1-120.ov.2.5 | $120$ | $2$ | $2$ | $1$ |
120.288.8-120.cg.1.50 | $120$ | $3$ | $3$ | $8$ |
120.384.7-120.cj.2.17 | $120$ | $4$ | $4$ | $7$ |
120.480.16-120.bi.2.3 | $120$ | $5$ | $5$ | $16$ |