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: | $\begin{bmatrix}23&98\\50&3\end{bmatrix}$, $\begin{bmatrix}53&22\\26&15\end{bmatrix}$, $\begin{bmatrix}63&50\\46&9\end{bmatrix}$, $\begin{bmatrix}99&38\\32&51\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 60.24.0.e.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
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ 3 x^{2} - 9 x y + 3 y^{2} - 20 z^{2} $ |
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 |
---|---|---|---|---|---|
24.24.0-12.a.1.1 | $24$ | $2$ | $2$ | $0$ | $0$ |
40.24.0-20.b.1.2 | $40$ | $2$ | $2$ | $0$ | $0$ |
120.24.0-12.a.1.3 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.24.0-20.b.1.4 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.24.0-60.b.1.4 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.24.0-60.b.1.5 | $120$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.144.4-60.h.1.15 | $120$ | $3$ | $3$ | $4$ |
120.192.3-60.h.1.15 | $120$ | $4$ | $4$ | $3$ |
120.240.8-60.h.1.2 | $120$ | $5$ | $5$ | $8$ |
120.288.7-60.bc.1.11 | $120$ | $6$ | $6$ | $7$ |
120.480.15-60.h.1.7 | $120$ | $10$ | $10$ | $15$ |