Invariants
Level: | $120$ | $\SL_2$-level: | $20$ | Newform level: | $180$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $1^{4}\cdot4^{2}\cdot5^{4}\cdot20^{2}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
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: | 20H1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}6&25\\65&86\end{bmatrix}$, $\begin{bmatrix}17&10\\18&29\end{bmatrix}$, $\begin{bmatrix}58&119\\17&90\end{bmatrix}$, $\begin{bmatrix}85&34\\36&43\end{bmatrix}$, $\begin{bmatrix}85&38\\114&109\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 60.72.1.ba.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: | 180.2.a.a |
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 |
---|---|---|---|---|---|---|
40.72.0-10.a.1.13 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.72.0-10.a.1.11 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
120.288.5-60.z.2.9 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-60.dd.2.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.gw.2.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-60.ii.2.5 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-60.im.2.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-60.kt.2.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-60.kv.2.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-60.kx.2.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-60.ld.2.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.vy.2.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cns.2.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.cor.2.5 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.dee.2.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.des.2.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.dfi.2.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.dgy.2.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.432.13-60.cx.1.31 | $120$ | $3$ | $3$ | $13$ | $?$ | not computed |