Invariants
Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
Genus: | $13 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $5^{8}\cdot10^{4}\cdot40^{4}$ | Cusp orbits | $4^{2}\cdot8$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 24$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 13$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 40G13 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}20&41\\69&16\end{bmatrix}$, $\begin{bmatrix}23&24\\76&7\end{bmatrix}$, $\begin{bmatrix}37&70\\30&17\end{bmatrix}$, $\begin{bmatrix}68&47\\15&32\end{bmatrix}$, $\begin{bmatrix}69&44\\26&103\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.240.13.bwg.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $768$ |
Full 120-torsion field degree: | $73728$ |
Rational points
This modular curve has no $\Q_p$ points for $p=13$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
40.240.5-40.be.1.14 | $40$ | $2$ | $2$ | $5$ | $2$ |
120.240.5-40.be.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ |
120.240.7-120.cy.1.33 | $120$ | $2$ | $2$ | $7$ | $?$ |
120.240.7-120.cy.1.41 | $120$ | $2$ | $2$ | $7$ | $?$ |
120.240.7-120.di.1.17 | $120$ | $2$ | $2$ | $7$ | $?$ |
120.240.7-120.di.1.49 | $120$ | $2$ | $2$ | $7$ | $?$ |