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 | $2^{6}\cdot4$ | ||
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: | $\begin{bmatrix}35&104\\58&69\end{bmatrix}$, $\begin{bmatrix}47&8\\118&21\end{bmatrix}$, $\begin{bmatrix}71&14\\46&51\end{bmatrix}$, $\begin{bmatrix}111&8\\32&39\end{bmatrix}$, $\begin{bmatrix}116&41\\19&18\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.ss.4 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $12$ |
Cyclic 120-torsion field degree: | $384$ |
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 |
---|---|---|---|---|---|---|
12.96.0-12.c.3.3 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.96.0-12.c.3.9 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.dr.2.21 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.dr.2.24 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-120.zx.1.45 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.zx.1.61 | $120$ | $2$ | $2$ | $1$ | $?$ | 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.ly.3.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.rp.2.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.ta.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.tf.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.wq.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.xc.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.xs.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.xz.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgu.4.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgz.2.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhb.2.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhi.2.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.biq.1.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.biv.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bjv.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bkc.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |