Invariants
Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $3 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $3^{4}\cdot6^{2}\cdot24^{2}$ | Cusp orbits | $2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24L3 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}19&118\\86&43\end{bmatrix}$, $\begin{bmatrix}31&8\\110&53\end{bmatrix}$, $\begin{bmatrix}78&65\\91&12\end{bmatrix}$, $\begin{bmatrix}98&85\\95&32\end{bmatrix}$, $\begin{bmatrix}109&74\\62&89\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.72.3.ccy.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $245760$ |
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 |
---|---|---|---|---|---|
24.72.2-24.cw.1.13 | $24$ | $2$ | $2$ | $2$ | $0$ |
60.72.1-60.i.1.2 | $60$ | $2$ | $2$ | $1$ | $0$ |
120.72.1-60.i.1.9 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.72.2-24.cw.1.14 | $120$ | $2$ | $2$ | $2$ | $?$ |
120.72.2-120.cz.1.10 | $120$ | $2$ | $2$ | $2$ | $?$ |
120.72.2-120.cz.1.33 | $120$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.