Invariants
Level: | $120$ | $\SL_2$-level: | $12$ | 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 | $4^{12}\cdot12^{12}$ | 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: | $\begin{bmatrix}27&50\\64&71\end{bmatrix}$, $\begin{bmatrix}35&96\\36&59\end{bmatrix}$, $\begin{bmatrix}65&52\\14&99\end{bmatrix}$, $\begin{bmatrix}89&76\\90&1\end{bmatrix}$, $\begin{bmatrix}117&32\\76&107\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 120.384.5-120.kl.4.1, 120.384.5-120.kl.4.2, 120.384.5-120.kl.4.3, 120.384.5-120.kl.4.4, 120.384.5-120.kl.4.5, 120.384.5-120.kl.4.6, 120.384.5-120.kl.4.7, 120.384.5-120.kl.4.8, 120.384.5-120.kl.4.9, 120.384.5-120.kl.4.10, 120.384.5-120.kl.4.11, 120.384.5-120.kl.4.12, 120.384.5-120.kl.4.13, 120.384.5-120.kl.4.14, 120.384.5-120.kl.4.15, 120.384.5-120.kl.4.16 |
Cyclic 120-isogeny field degree: | $24$ |
Cyclic 120-torsion field degree: | $384$ |
Full 120-torsion field degree: | $184320$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.96.1.cp.2 | $24$ | $2$ | $2$ | $1$ | $1$ |
60.96.1.e.4 | $60$ | $2$ | $2$ | $1$ | $1$ |
120.96.1.lx.1 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.96.3.ej.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.96.3.fi.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.96.3.fl.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.96.3.ft.1 | $120$ | $2$ | $2$ | $3$ | $?$ |