Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $8^{24}$ | Cusp orbits | $4^{4}\cdot8$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8A5 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}9&10\\104&59\end{bmatrix}$, $\begin{bmatrix}43&20\\108&91\end{bmatrix}$, $\begin{bmatrix}47&74\\44&1\end{bmatrix}$, $\begin{bmatrix}59&30\\0&77\end{bmatrix}$, $\begin{bmatrix}61&22\\72&11\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 120.384.5-120.u.1.1, 120.384.5-120.u.1.2, 120.384.5-120.u.1.3, 120.384.5-120.u.1.4, 120.384.5-120.u.1.5, 120.384.5-120.u.1.6, 120.384.5-120.u.1.7, 120.384.5-120.u.1.8, 120.384.5-120.u.1.9, 120.384.5-120.u.1.10, 120.384.5-120.u.1.11, 120.384.5-120.u.1.12, 120.384.5-120.u.1.13, 120.384.5-120.u.1.14, 120.384.5-120.u.1.15, 120.384.5-120.u.1.16 |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $184320$ |
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 |
---|---|---|---|---|---|
24.96.1.a.1 | $24$ | $2$ | $2$ | $1$ | $1$ |
40.96.1.a.2 | $40$ | $2$ | $2$ | $1$ | $0$ |
120.96.1.bp.1 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.96.3.p.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.96.3.bu.2 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.96.3.by.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.96.3.cc.2 | $120$ | $2$ | $2$ | $3$ | $?$ |