Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $384$ | $\PSL_2$-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 | $4^{6}$ | ||
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: | $\begin{bmatrix}73&116\\52&25\end{bmatrix}$, $\begin{bmatrix}81&86\\116&23\end{bmatrix}$, $\begin{bmatrix}105&22\\104&79\end{bmatrix}$, $\begin{bmatrix}113&94\\116&59\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.192.5.hd.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $384$ |
Full 120-torsion field degree: | $92160$ |
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 |
---|---|---|---|---|---|
24.192.1-24.s.1.5 | $24$ | $2$ | $2$ | $1$ | $0$ |
40.192.1-40.o.1.1 | $40$ | $2$ | $2$ | $1$ | $1$ |
120.192.1-40.o.1.9 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-24.s.1.9 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.cs.2.4 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.cs.2.19 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.3-120.bx.2.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.bx.2.8 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.bz.1.16 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.bz.1.21 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.ce.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.ce.1.20 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.cv.1.4 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.cv.1.10 | $120$ | $2$ | $2$ | $3$ | $?$ |