Invariants
Level: | $120$ | $\SL_2$-level: | $24$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $1^{4}\cdot2^{2}\cdot3^{4}\cdot6^{2}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $2^{4}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24J1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}9&76\\14&119\end{bmatrix}$, $\begin{bmatrix}50&81\\97&22\end{bmatrix}$, $\begin{bmatrix}93&98\\110&117\end{bmatrix}$, $\begin{bmatrix}99&14\\44&21\end{bmatrix}$, $\begin{bmatrix}110&117\\39&104\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.ti.3 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $12$ |
Cyclic 120-torsion field degree: | $192$ |
Full 120-torsion field degree: | $184320$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
24.96.1-24.ix.1.22 | $24$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
120.96.0-120.dr.2.6 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.dr.2.25 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ds.2.9 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ds.2.25 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-24.ix.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
120.384.5-120.qv.2.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.rs.4.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.vf.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.vi.3.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.xh.2.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.xm.2.5 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.yv.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.za.1.5 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhk.4.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhq.4.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bia.2.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.big.3.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bjw.2.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bkc.2.5 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bkm.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bks.1.5 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |