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: | $\begin{bmatrix}11&82\\26&3\end{bmatrix}$, $\begin{bmatrix}19&68\\84&5\end{bmatrix}$, $\begin{bmatrix}39&68\\38&57\end{bmatrix}$, $\begin{bmatrix}91&56\\18&35\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.192.5.og.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 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 |
---|---|---|---|---|---|
24.192.3-24.bt.2.6 | $24$ | $2$ | $2$ | $3$ | $0$ |
60.192.1-60.f.4.3 | $60$ | $2$ | $2$ | $1$ | $0$ |
120.192.1-60.f.4.15 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.lf.2.6 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.lf.2.32 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.lp.3.6 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.1-120.lp.3.28 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.192.3-24.bt.2.8 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.dr.1.29 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.dr.1.31 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.gh.2.5 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.gh.2.28 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.gi.2.22 | $120$ | $2$ | $2$ | $3$ | $?$ |
120.192.3-120.gi.2.28 | $120$ | $2$ | $2$ | $3$ | $?$ |