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: | 24W3 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}2&81\\69&74\end{bmatrix}$, $\begin{bmatrix}68&19\\81&82\end{bmatrix}$, $\begin{bmatrix}73&56\\90&23\end{bmatrix}$, $\begin{bmatrix}73&92\\52&9\end{bmatrix}$, $\begin{bmatrix}81&62\\14&45\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.3.ta.2 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.iu.1.18 | $24$ | $2$ | $2$ | $1$ | $0$ |
120.96.0-120.ds.1.37 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.96.0-120.ds.1.48 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.96.1-24.iu.1.25 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.96.2-120.i.2.37 | $120$ | $2$ | $2$ | $2$ | $?$ |
120.96.2-120.i.2.50 | $120$ | $2$ | $2$ | $2$ | $?$ |
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.qq.4.16 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.rm.4.15 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.uy.2.9 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.vc.3.14 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.vm.3.2 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.vp.4.5 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.yu.2.5 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.za.3.7 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bah.3.2 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.ban.4.11 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bax.3.5 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bbd.2.14 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bct.4.2 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bcz.4.9 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bdj.4.9 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bdp.3.13 | $120$ | $2$ | $2$ | $5$ |