Invariants
Level: | $120$ | $\SL_2$-level: | $12$ | 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 | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | 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: | 12V1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}19&108\\16&103\end{bmatrix}$, $\begin{bmatrix}67&0\\95&71\end{bmatrix}$, $\begin{bmatrix}109&108\\102&85\end{bmatrix}$, $\begin{bmatrix}115&48\\13&5\end{bmatrix}$, $\begin{bmatrix}119&96\\110&91\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.ru.1 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 |
---|---|---|---|---|---|---|
24.96.0-24.bu.3.5 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
60.96.1-60.l.1.9 | $60$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
120.96.0-24.bu.3.13 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ds.1.2 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ds.1.29 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-60.l.1.11 | $120$ | $2$ | $2$ | $1$ | $?$ | 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.zk.4.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.zn.4.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.baa.3.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bad.3.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bax.3.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bbc.3.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bbf.4.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bbk.4.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgd.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgi.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgt.4.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgy.4.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhs.4.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhv.4.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bia.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bid.1.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |