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: | 24U3 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}43&60\\43&77\end{bmatrix}$, $\begin{bmatrix}73&108\\23&89\end{bmatrix}$, $\begin{bmatrix}73&108\\39&91\end{bmatrix}$, $\begin{bmatrix}89&108\\80&107\end{bmatrix}$, $\begin{bmatrix}91&84\\113&95\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.3.ne.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $12$ |
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 |
---|---|---|---|---|---|
24.96.0-24.bs.2.23 | $24$ | $2$ | $2$ | $0$ | $0$ |
120.96.0-24.bs.2.21 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.96.1-60.l.1.11 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.96.1-60.l.1.15 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.96.2-120.i.2.46 | $120$ | $2$ | $2$ | $2$ | $?$ |
120.96.2-120.i.2.55 | $120$ | $2$ | $2$ | $2$ | $?$ |
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.zj.1.3 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.zj.3.12 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.zk.1.3 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.zk.3.7 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.zz.1.6 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.zz.3.6 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.baa.1.3 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.baa.3.3 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bax.1.14 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bax.3.14 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bay.1.13 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bay.3.13 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bbf.1.16 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bbf.3.10 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bbg.1.15 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bbg.3.9 | $120$ | $2$ | $2$ | $5$ |