Invariants
Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
Genus: | $17 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $20^{4}\cdot40^{4}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 32$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 17$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 40A17 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}17&104\\4&65\end{bmatrix}$, $\begin{bmatrix}91&3\\4&1\end{bmatrix}$, $\begin{bmatrix}91&84\\100&23\end{bmatrix}$, $\begin{bmatrix}103&64\\72&19\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.240.17.vg.1 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 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 |
---|---|---|---|---|---|
$X_{S_4}(5)$ | $5$ | $96$ | $48$ | $0$ | $0$ |
24.96.1-24.eu.1.4 | $24$ | $5$ | $5$ | $1$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.96.1-24.eu.1.4 | $24$ | $5$ | $5$ | $1$ | $0$ |
40.240.8-20.f.1.4 | $40$ | $2$ | $2$ | $8$ | $2$ |
120.240.8-20.f.1.4 | $120$ | $2$ | $2$ | $8$ | $?$ |
120.240.8-120.cw.1.2 | $120$ | $2$ | $2$ | $8$ | $?$ |
120.240.8-120.cw.1.15 | $120$ | $2$ | $2$ | $8$ | $?$ |
120.240.9-120.y.1.3 | $120$ | $2$ | $2$ | $9$ | $?$ |
120.240.9-120.y.1.16 | $120$ | $2$ | $2$ | $9$ | $?$ |