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: | $\begin{bmatrix}29&114\\42&35\end{bmatrix}$, $\begin{bmatrix}43&60\\94&71\end{bmatrix}$, $\begin{bmatrix}71&28\\50&81\end{bmatrix}$, $\begin{bmatrix}105&106\\112&9\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.192.5.kh.4 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.cn.4.5 | $24$ | $2$ | $2$ | $1$ | $0$ |
60.192.3-60.p.1.12 | $60$ | $2$ | $2$ | $3$ | $0$ |
120.192.1-24.cn.4.14 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.lq.3.10 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.lq.3.29 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.lv.1.14 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.lv.1.24 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.3-60.p.1.12 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.eg.1.2 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.eg.1.6 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.fg.1.18 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.fg.1.29 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.fv.1.4 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.fv.1.23 | $120$ | $2$ | $2$ | $3$ | $?$ |