Invariants
Level: | $120$ | $\SL_2$-level: | $4$ | ||||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $4^{6}$ | Cusp orbits | $2^{3}$ | ||
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: | 4G0 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}7&100\\6&101\end{bmatrix}$, $\begin{bmatrix}17&106\\72&85\end{bmatrix}$, $\begin{bmatrix}55&98\\72&61\end{bmatrix}$, $\begin{bmatrix}87&76\\118&1\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.24.0.k.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $96$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $737280$ |
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 |
---|---|---|---|---|---|
12.24.0-12.a.1.2 | $12$ | $2$ | $2$ | $0$ | $0$ |
40.24.0-40.b.1.1 | $40$ | $2$ | $2$ | $0$ | $0$ |
120.24.0-12.a.1.3 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.24.0-40.b.1.5 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.24.0-120.b.1.6 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.24.0-120.b.1.9 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.144.4-120.r.1.2 | $120$ | $3$ | $3$ | $4$ |
120.192.3-120.ef.1.5 | $120$ | $4$ | $4$ | $3$ |
120.240.8-120.r.1.14 | $120$ | $5$ | $5$ | $8$ |
120.288.7-120.eo.1.2 | $120$ | $6$ | $6$ | $7$ |
120.480.15-120.r.1.16 | $120$ | $10$ | $10$ | $15$ |