Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | 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: | $16$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $2^{2}\cdot4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}15&92\\68&33\end{bmatrix}$, $\begin{bmatrix}19&40\\30&83\end{bmatrix}$, $\begin{bmatrix}41&48\\36&109\end{bmatrix}$, $\begin{bmatrix}113&24\\72&55\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.hd.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $184320$ |
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 |
---|---|---|---|---|---|---|
24.96.0-24.m.2.14 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
40.96.1-40.be.2.13 | $40$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
120.96.0-120.k.2.3 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.k.2.25 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-24.m.2.2 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bq.2.13 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bq.2.25 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bu.1.14 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.bu.1.18 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-40.be.2.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.bx.1.19 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.bx.1.31 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.dk.2.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.dk.2.12 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |