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 | $2^{4}\cdot4^{2}\cdot8$ | ||
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: | $\begin{bmatrix}1&68\\8&41\end{bmatrix}$, $\begin{bmatrix}19&52\\12&47\end{bmatrix}$, $\begin{bmatrix}43&86\\116&93\end{bmatrix}$, $\begin{bmatrix}83&48\\4&67\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.192.5.hn.2 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 $\Q_p$ points for $p=29$, 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.x.2.4 | $24$ | $2$ | $2$ | $1$ | $0$ |
40.192.3-40.be.1.2 | $40$ | $2$ | $2$ | $3$ | $0$ |
120.192.1-24.x.2.10 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.bn.2.1 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.bn.2.20 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.cz.1.10 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.cz.1.21 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.3-40.be.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.bo.2.15 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.bo.2.19 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.bw.3.16 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.bw.3.17 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.cb.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.cb.1.8 | $120$ | $2$ | $2$ | $3$ | $?$ |