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: | $\begin{bmatrix}7&68\\32&45\end{bmatrix}$, $\begin{bmatrix}37&36\\70&7\end{bmatrix}$, $\begin{bmatrix}37&100\\8&33\end{bmatrix}$, $\begin{bmatrix}77&0\\110&61\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 24.96.1.bw.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 $ | $=$ | $ 2 y^{2} + 2 z^{2} - w^{2} $ |
| $=$ | $x^{2} - y^{2} + 2 z^{2} + 2 w^{2}$ |
Rational points
This modular curve has no real points, and therefore no 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 $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle 2^4\,\frac{(4z^{4}-4z^{3}w+2z^{2}w^{2}-2zw^{3}+w^{4})^{3}(4z^{4}+4z^{3}w+2z^{2}w^{2}+2zw^{3}+w^{4})^{3}}{w^{8}z^{8}(2z^{2}-w^{2})^{2}(2z^{2}+w^{2})^{2}}$ |
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.h.1.7 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 120.96.0-8.h.1.1 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.h.2.7 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.h.2.13 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.j.2.2 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.j.2.9 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.z.1.6 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.z.1.13 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.1-24.bh.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bh.1.16 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bj.2.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bj.2.13 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bs.1.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bs.1.15 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |