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: | $\begin{bmatrix}68&43\\89&2\end{bmatrix}$, $\begin{bmatrix}88&23\\119&62\end{bmatrix}$, $\begin{bmatrix}88&65\\105&38\end{bmatrix}$, $\begin{bmatrix}94&33\\103&104\end{bmatrix}$, $\begin{bmatrix}99&2\\50&51\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.72.1.bn.2 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 no real points, and therefore no 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.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | 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.dn.2.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.fw.2.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.nm.2.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.nq.2.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bjs.2.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bju.2.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bkn.2.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bkp.2.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.blx.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bma.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bmr.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bmt.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bqe.1.5 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bqg.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.bqz.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.brb.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.432.13-120.eh.1.23 | $120$ | $3$ | $3$ | $13$ | $?$ | not computed |