Invariants
Level: | $120$ | $\SL_2$-level: | $12$ | 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 | $4^{12}\cdot12^{12}$ | Cusp orbits | $2^{2}\cdot4^{5}$ | ||
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: | 12E5 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}25&18\\112&83\end{bmatrix}$, $\begin{bmatrix}29&102\\38&31\end{bmatrix}$, $\begin{bmatrix}75&32\\8&99\end{bmatrix}$, $\begin{bmatrix}99&10\\20&43\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.192.5.ja.2 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $24$ |
Cyclic 120-torsion field degree: | $384$ |
Full 120-torsion field degree: | $92160$ |
Rational points
This modular curve has no $\Q_p$ points for $p=23$, 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.cl.1.9 | $24$ | $2$ | $2$ | $1$ | $0$ |
60.192.1-60.f.4.3 | $60$ | $2$ | $2$ | $1$ | $0$ |
120.192.1-60.f.4.12 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-24.cl.1.5 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.lo.3.14 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.lo.3.28 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.3-120.du.1.29 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.du.1.31 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.fc.1.14 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.fc.1.26 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.fk.1.8 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.fk.1.12 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.fo.1.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.fo.1.27 | $120$ | $2$ | $2$ | $3$ | $?$ |