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: | $\begin{bmatrix}3&20\\80&9\end{bmatrix}$, $\begin{bmatrix}7&0\\114&91\end{bmatrix}$, $\begin{bmatrix}79&110\\100&51\end{bmatrix}$, $\begin{bmatrix}111&38\\64&53\end{bmatrix}$, $\begin{bmatrix}111&94\\88&15\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 120.384.5-120.km.3.1, 120.384.5-120.km.3.2, 120.384.5-120.km.3.3, 120.384.5-120.km.3.4, 120.384.5-120.km.3.5, 120.384.5-120.km.3.6, 120.384.5-120.km.3.7, 120.384.5-120.km.3.8, 120.384.5-120.km.3.9, 120.384.5-120.km.3.10, 120.384.5-120.km.3.11, 120.384.5-120.km.3.12, 120.384.5-120.km.3.13, 120.384.5-120.km.3.14, 120.384.5-120.km.3.15, 120.384.5-120.km.3.16 |
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.h.3 | $60$ | $2$ | $2$ | $1$ | $1$ |
120.96.1.lo.2 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.96.3.ek.1 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.96.3.fi.2 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.96.3.fk.2 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.96.3.fu.2 | $120$ | $2$ | $2$ | $3$ | $?$ |