Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $576$ | ||
| 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: | $\begin{bmatrix}3&92\\110&111\end{bmatrix}$, $\begin{bmatrix}43&60\\48&83\end{bmatrix}$, $\begin{bmatrix}83&84\\86&17\end{bmatrix}$, $\begin{bmatrix}101&52\\46&33\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 24.96.1.bl.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: | 576.2.a.c |
Models
Embedded model Embedded model in $\mathbb{P}^{3}$
| $ 0 $ | $=$ | $ x^{2} - y^{2} - z^{2} + w^{2} $ |
| $=$ | $3 x^{2} + 3 y^{2} - w^{2}$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Maps to other modular curves
$j$-invariant map of degree 96 from the embedded model of this modular curve to the modular curve $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{2^4}{3^2}\cdot\frac{(81z^{8}-216z^{6}w^{2}+180z^{4}w^{4}-48z^{2}w^{6}+16w^{8})^{3}}{w^{8}z^{4}(3z^{2}-4w^{2})^{2}(3z^{2}-2w^{2})^{4}}$ |
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 40.96.0-8.e.1.8 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 120.96.0-24.d.1.6 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.d.1.15 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-8.e.1.3 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.t.2.6 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.t.2.14 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.v.1.12 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.v.1.16 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.1-24.bb.1.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bb.1.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bg.2.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bg.2.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bi.2.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bi.2.16 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |