Invariants
Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $2^{4}\cdot6^{4}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $2^{6}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24V3 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}21&118\\80&61\end{bmatrix}$, $\begin{bmatrix}31&78\\100&11\end{bmatrix}$, $\begin{bmatrix}73&101\\64&9\end{bmatrix}$, $\begin{bmatrix}113&37\\8&15\end{bmatrix}$, $\begin{bmatrix}119&115\\68&33\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.3.qf.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $12$ |
Cyclic 120-torsion field degree: | $192$ |
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 |
---|---|---|---|---|---|
24.96.1-24.ix.1.22 | $24$ | $2$ | $2$ | $1$ | $0$ |
120.48.0-120.dz.1.7 | $120$ | $4$ | $4$ | $0$ | $?$ |
120.96.1-24.ix.1.14 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.96.1-120.zo.1.9 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.96.1-120.zo.1.32 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.96.1-120.zx.1.26 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.96.1-120.zx.1.41 | $120$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
120.384.5-120.bde.1.6 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bde.2.5 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bde.3.10 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bde.4.9 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bdi.1.4 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bdi.2.3 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bdi.3.6 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bdi.4.5 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bjy.1.6 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bjy.2.5 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bjy.3.10 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bjy.4.9 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bkc.1.6 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bkc.2.5 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bkc.3.10 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bkc.4.9 | $120$ | $2$ | $2$ | $5$ |