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: | $\begin{bmatrix}3&46\\38&35\end{bmatrix}$, $\begin{bmatrix}7&30\\80&29\end{bmatrix}$, $\begin{bmatrix}21&2\\40&67\end{bmatrix}$, $\begin{bmatrix}50&51\\9&116\end{bmatrix}$, $\begin{bmatrix}105&56\\86&51\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.tb.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $12$ |
Cyclic 120-torsion field degree: | $192$ |
Full 120-torsion field degree: | $184320$ |
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.iu.1.18 | $24$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
120.96.0-120.dq.1.13 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.dq.1.34 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ds.2.9 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ds.2.19 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-24.iu.1.4 | $120$ | $2$ | $2$ | $1$ | $?$ | 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.qq.3.20 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.re.2.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.uy.1.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.vb.4.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.vm.3.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.vn.3.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.yu.3.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.yy.4.9 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhd.2.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhf.3.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bht.4.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhv.3.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bjp.3.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bjr.4.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bkf.4.9 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bkh.4.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |