Invariants
Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
Genus: | $8 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (none of which are rational) | Cusp widths | $20^{6}$ | Cusp orbits | $2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 14$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 8$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 20A8 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}27&34\\80&113\end{bmatrix}$, $\begin{bmatrix}83&110\\44&1\end{bmatrix}$, $\begin{bmatrix}91&114\\10&97\end{bmatrix}$, $\begin{bmatrix}95&16\\78&25\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.120.8.f.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $96$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $147456$ |
Rational points
This modular curve has no $\Q_p$ points for $p=7$, and therefore no rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
Factor curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
$X_{S_4}(5)$ | $5$ | $48$ | $24$ | $0$ | $0$ |
24.48.0-24.f.1.2 | $24$ | $5$ | $5$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.48.0-24.f.1.2 | $24$ | $5$ | $5$ | $0$ | $0$ |
40.120.4-40.b.1.8 | $40$ | $2$ | $2$ | $4$ | $0$ |
120.120.4-40.b.1.4 | $120$ | $2$ | $2$ | $4$ | $?$ |
60.120.4-60.a.1.1 | $60$ | $2$ | $2$ | $4$ | $1$ |
120.120.4-60.a.1.6 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.120.4-120.b.1.4 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.120.4-120.b.1.14 | $120$ | $2$ | $2$ | $4$ | $?$ |