Invariants
Level: | $120$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $1^{4}\cdot4^{2}\cdot5^{4}\cdot20^{2}$ | Cusp orbits | $2^{2}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 72$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 20H1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}62&19\\53&108\end{bmatrix}$, $\begin{bmatrix}64&37\\37&74\end{bmatrix}$, $\begin{bmatrix}77&0\\36&91\end{bmatrix}$, $\begin{bmatrix}85&52\\76&81\end{bmatrix}$, $\begin{bmatrix}94&85\\81&68\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.72.1.bk.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $16$ |
Cyclic 120-torsion field degree: | $512$ |
Full 120-torsion field degree: | $245760$ |
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 |
---|---|---|---|---|---|---|
40.72.1-20.b.1.9 | $40$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
120.72.1-20.b.1.7 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
120.288.5-120.dh.2.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fx.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.nf.2.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.nj.2.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bjz.2.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bkb.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bkg.2.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bki.2.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.blw.2.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bmb.2.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bmk.2.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bmm.2.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bql.2.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bqn.2.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bqs.2.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bqu.2.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.432.13-120.ee.2.23 | $120$ | $3$ | $3$ | $13$ | $?$ | not computed |