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: | $16$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12V1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}19&96\\27&49\end{bmatrix}$, $\begin{bmatrix}25&36\\38&91\end{bmatrix}$, $\begin{bmatrix}43&12\\70&89\end{bmatrix}$, $\begin{bmatrix}43&36\\39&91\end{bmatrix}$, $\begin{bmatrix}49&24\\20&67\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.rv.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 is an elliptic curve, but the rank has not been computed
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.3.3 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ds.1.48 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ds.1.55 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-120.zf.1.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.zf.1.24 | $120$ | $2$ | $2$ | $1$ | $?$ | 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.zl.4.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.zq.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bab.3.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bag.2.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bba.3.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bbd.2.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bbi.4.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bbl.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgg.4.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgj.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgw.3.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bgz.2.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bht.3.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bhy.2.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.bib.4.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.big.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |