Invariants
Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
Genus: | $7 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $10^{4}\cdot20^{4}$ | Cusp orbits | $2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 12$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 7$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 20B7 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}1&32\\90&49\end{bmatrix}$, $\begin{bmatrix}23&88\\78&7\end{bmatrix}$, $\begin{bmatrix}63&26\\56&45\end{bmatrix}$, $\begin{bmatrix}63&112\\112&57\end{bmatrix}$, $\begin{bmatrix}75&64\\14&103\end{bmatrix}$, $\begin{bmatrix}83&28\\98&69\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.120.7.f.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $96$ |
Cyclic 120-torsion field degree: | $3072$ |
Full 120-torsion field degree: | $147456$ |
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 |
---|---|---|---|---|---|
40.120.3-10.a.1.2 | $40$ | $2$ | $2$ | $3$ | $0$ |
60.120.3-10.a.1.4 | $60$ | $2$ | $2$ | $3$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.