Invariants
| Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $1568$ | ||
| 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
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}17&24\\216&131\end{bmatrix}$, $\begin{bmatrix}67&28\\180&3\end{bmatrix}$, $\begin{bmatrix}79&32\\12&33\end{bmatrix}$, $\begin{bmatrix}137&144\\276&215\end{bmatrix}$, $\begin{bmatrix}243&20\\268&271\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 56.96.1.s.2 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $96$ |
| Cyclic 280-torsion field degree: | $9216$ |
| Full 280-torsion field degree: | $7741440$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 1568.2.a.e |
Models
Embedded model Embedded model in $\mathbb{P}^{3}$
| $ 0 $ | $=$ | $ x^{2} - y^{2} + z^{2} $ |
| $=$ | $7 x^{2} + 7 y^{2} + w^{2}$ |
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 $X(1)$ :
| $\displaystyle j$ | $=$ | $\displaystyle \frac{2^8}{7^4}\cdot\frac{(2401z^{8}-49z^{4}w^{4}+w^{8})^{3}}{w^{8}z^{8}(7z^{2}-w^{2})^{2}(7z^{2}+w^{2})^{2}}$ |
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.1.10 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 280.96.0-8.b.1.3 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 280.96.0-56.c.1.5 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 280.96.0-56.c.1.18 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 280.96.0-56.t.2.5 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 280.96.0-56.t.2.10 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 280.96.0-56.v.1.3 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 280.96.0-56.v.1.14 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
| 280.96.1-56.o.2.3 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 280.96.1-56.o.2.13 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 280.96.1-56.bd.1.11 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 280.96.1-56.bd.1.14 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 280.96.1-56.bf.2.12 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
| 280.96.1-56.bf.2.13 | $280$ | $2$ | $2$ | $1$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 280.384.5-56.q.2.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.384.5-56.s.4.5 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.384.5-56.u.1.7 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.384.5-56.v.2.5 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.384.5-280.fo.2.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.384.5-280.fq.2.15 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.384.5-280.fv.2.14 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 280.384.5-280.fx.2.14 | $280$ | $2$ | $2$ | $5$ | $?$ | not computed |