Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8G1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}31&78\\40&53\end{bmatrix}$, $\begin{bmatrix}61&66\\48&59\end{bmatrix}$, $\begin{bmatrix}71&96\\88&55\end{bmatrix}$, $\begin{bmatrix}89&64\\112&31\end{bmatrix}$, $\begin{bmatrix}97&74\\4&105\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.1.ec.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $368640$ |
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 |
---|---|---|---|---|---|---|
24.48.0-8.d.2.9 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
40.48.0-8.d.2.1 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.48.0-120.u.2.26 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.0-120.u.2.34 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.1-120.d.1.29 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.48.1-120.d.1.32 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
120.192.1-120.a.2.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.bz.2.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ej.2.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.er.2.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ic.2.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ik.2.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.jz.2.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.kh.2.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ly.2.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.mg.2.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.nv.2.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.od.2.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.pa.2.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.pi.2.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.py.2.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qc.2.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.288.9-120.to.1.34 | $120$ | $3$ | $3$ | $9$ | $?$ | not computed |
120.384.9-120.km.1.33 | $120$ | $4$ | $4$ | $9$ | $?$ | not computed |
120.480.17-120.gg.1.25 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |