Invariants
Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
Genus: | $16 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $20^{8}\cdot40^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 16$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 16$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 40A16 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}1&12\\116&79\end{bmatrix}$, $\begin{bmatrix}37&80\\76&49\end{bmatrix}$, $\begin{bmatrix}47&88\\48&113\end{bmatrix}$, $\begin{bmatrix}55&8\\44&95\end{bmatrix}$, $\begin{bmatrix}61&46\\112&75\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.240.16.bb.2 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $73728$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal 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 |
---|---|---|---|---|---|
$X_{S_4}(5)$ | $5$ | $96$ | $48$ | $0$ | $0$ |
24.96.0-24.n.2.10 | $24$ | $5$ | $5$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.96.0-24.n.2.10 | $24$ | $5$ | $5$ | $0$ | $0$ |
40.240.8-40.n.2.9 | $40$ | $2$ | $2$ | $8$ | $0$ |
120.240.8-120.e.1.32 | $120$ | $2$ | $2$ | $8$ | $?$ |
120.240.8-120.e.1.35 | $120$ | $2$ | $2$ | $8$ | $?$ |
120.240.8-40.n.2.12 | $120$ | $2$ | $2$ | $8$ | $?$ |
120.240.8-120.bd.1.28 | $120$ | $2$ | $2$ | $8$ | $?$ |
120.240.8-120.bd.1.45 | $120$ | $2$ | $2$ | $8$ | $?$ |