Invariants
Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $5 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot10^{4}\cdot20^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 20I5 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}19&110\\15&31\end{bmatrix}$, $\begin{bmatrix}53&70\\76&19\end{bmatrix}$, $\begin{bmatrix}73&10\\83&1\end{bmatrix}$, $\begin{bmatrix}87&100\\100&119\end{bmatrix}$, $\begin{bmatrix}97&110\\18&41\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 120.288.5-120.enq.1.1, 120.288.5-120.enq.1.2, 120.288.5-120.enq.1.3, 120.288.5-120.enq.1.4, 120.288.5-120.enq.1.5, 120.288.5-120.enq.1.6, 120.288.5-120.enq.1.7, 120.288.5-120.enq.1.8, 120.288.5-120.enq.1.9, 120.288.5-120.enq.1.10, 120.288.5-120.enq.1.11, 120.288.5-120.enq.1.12, 120.288.5-120.enq.1.13, 120.288.5-120.enq.1.14, 120.288.5-120.enq.1.15, 120.288.5-120.enq.1.16 |
Cyclic 120-isogeny field degree: | $16$ |
Cyclic 120-torsion field degree: | $256$ |
Full 120-torsion field degree: | $245760$ |
Rational points
This modular curve has no $\Q_p$ points for $p=19$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
40.72.3.eq.2 | $40$ | $2$ | $2$ | $3$ | $0$ |
60.72.1.cf.1 | $60$ | $2$ | $2$ | $1$ | $1$ |
120.72.1.hx.2 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.72.1.nn.2 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.72.3.edz.2 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.72.3.eeh.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.72.3.egp.1 | $120$ | $2$ | $2$ | $3$ | $?$ |