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: | $\begin{bmatrix}25&12\\104&107\end{bmatrix}$, $\begin{bmatrix}25&72\\31&37\end{bmatrix}$, $\begin{bmatrix}43&48\\66&119\end{bmatrix}$, $\begin{bmatrix}89&48\\19&7\end{bmatrix}$, $\begin{bmatrix}95&48\\96&1\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.3.rc.2 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 |
---|---|---|---|---|---|
24.96.2-24.g.2.27 | $24$ | $2$ | $2$ | $2$ | $0$ |
120.96.0-120.dq.2.20 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.96.0-120.dq.2.39 | $120$ | $2$ | $2$ | $0$ | $?$ |
120.96.1-60.l.1.11 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.96.1-60.l.1.15 | $120$ | $2$ | $2$ | $1$ | $?$ |
120.96.2-24.g.2.21 | $120$ | $2$ | $2$ | $2$ | $?$ |
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.bgh.2.9 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bgh.4.12 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bgi.2.3 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bgi.4.7 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bgx.2.10 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bgx.4.10 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bgy.2.3 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bgy.4.3 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bhv.2.15 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bhv.4.15 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bhw.2.13 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bhw.4.13 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bid.2.16 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bid.4.13 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bie.2.15 | $120$ | $2$ | $2$ | $5$ |
120.384.5-120.bie.4.9 | $120$ | $2$ | $2$ | $5$ |