Invariants
| Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $288$ | ||
| 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 | $2^{4}\cdot4^{2}$ | ||
| 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: | $\begin{bmatrix}27&100\\100&31\end{bmatrix}$, $\begin{bmatrix}31&64\\60&103\end{bmatrix}$, $\begin{bmatrix}37&68\\8&63\end{bmatrix}$, $\begin{bmatrix}49&88\\96&115\end{bmatrix}$, $\begin{bmatrix}55&112\\104&3\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 24.96.1.s.2 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: | 288.2.a.d |
Models
Embedded model Embedded model in $\mathbb{P}^{3}$
| $ 0 $ | $=$ | $ x^{2} - y^{2} + z^{2} $ |
| $=$ | $3 x^{2} + 3 y^{2} + w^{2}$ |
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 $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{2^8}{3^4}\cdot\frac{(81z^{8}-9z^{4}w^{4}+w^{8})^{3}}{w^{8}z^{8}(3z^{2}-w^{2})^{2}(3z^{2}+w^{2})^{2}}$ |
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.b.1.11 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 120.96.0-8.b.1.8 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.c.1.2 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.c.1.16 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.u.1.2 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.u.1.15 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.w.1.4 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.0-24.w.1.13 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 120.96.1-24.o.2.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.o.2.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bd.1.2 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bd.1.7 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bf.2.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 120.96.1-24.bf.2.9 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 120.384.5-24.y.2.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-24.ba.4.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-24.bc.1.2 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-24.bd.2.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.gy.2.10 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.gz.1.10 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.hc.1.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.hd.2.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |