Invariants
Level: | $120$ | $\SL_2$-level: | $60$ | 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 | $10^{2}\cdot20^{2}\cdot30^{2}\cdot60^{2}$ | 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: | 60G17 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}25&42\\102&91\end{bmatrix}$, $\begin{bmatrix}42&5\\55&62\end{bmatrix}$, $\begin{bmatrix}59&54\\74&31\end{bmatrix}$, $\begin{bmatrix}70&21\\79&80\end{bmatrix}$, $\begin{bmatrix}95&6\\84&5\end{bmatrix}$, $\begin{bmatrix}98&75\\15&8\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.240.17.gii.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $24$ |
Cyclic 120-torsion field degree: | $768$ |
Full 120-torsion field degree: | $73728$ |
Rational points
This modular curve has no $\Q_p$ points for $p=53$, 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 |
---|---|---|---|---|---|
$X_{\mathrm{ns}}^+(5)$ | $5$ | $48$ | $24$ | $0$ | $0$ |
24.48.1-24.es.1.4 | $24$ | $10$ | $10$ | $1$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.48.1-24.es.1.4 | $24$ | $10$ | $10$ | $1$ | $0$ |
60.240.7-30.h.1.14 | $60$ | $2$ | $2$ | $7$ | $0$ |
120.240.7-30.h.1.10 | $120$ | $2$ | $2$ | $7$ | $?$ |