Invariants
Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $6^{4}\cdot12^{6}\cdot24^{2}$ | Cusp orbits | $2^{2}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 12$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24W7 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}45&34\\28&113\end{bmatrix}$, $\begin{bmatrix}61&80\\92&77\end{bmatrix}$, $\begin{bmatrix}65&42\\48&71\end{bmatrix}$, $\begin{bmatrix}65&68\\92&3\end{bmatrix}$, $\begin{bmatrix}69&58\\52&5\end{bmatrix}$, $\begin{bmatrix}95&116\\68&87\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.144.7.yv.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $122880$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
12.144.3-12.b.1.5 | $12$ | $2$ | $2$ | $3$ | $0$ |
120.144.3-12.b.1.6 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.144.4-120.bl.2.44 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.bl.2.92 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.bo.1.97 | $120$ | $2$ | $2$ | $4$ | $?$ |
120.144.4-120.bo.1.123 | $120$ | $2$ | $2$ | $4$ | $?$ |