Invariants
Level: | $280$ | $\SL_2$-level: | $56$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot14^{2}\cdot28^{2}$ | Cusp orbits | $2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 28E5 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}27&238\\71&151\end{bmatrix}$, $\begin{bmatrix}59&42\\189&159\end{bmatrix}$, $\begin{bmatrix}163&140\\85&83\end{bmatrix}$, $\begin{bmatrix}221&84\\126&201\end{bmatrix}$, $\begin{bmatrix}275&14\\246&249\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 140.96.5.m.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $24$ |
Cyclic 280-torsion field degree: | $2304$ |
Full 280-torsion field degree: | $7741440$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
56.96.2-28.b.1.6 | $56$ | $2$ | $2$ | $2$ | $0$ |
280.24.0-140.e.1.4 | $280$ | $8$ | $8$ | $0$ | $?$ |
280.96.2-28.b.1.15 | $280$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
280.384.11-280.kk.1.3 | $280$ | $2$ | $2$ | $11$ |
280.384.11-280.kk.1.12 | $280$ | $2$ | $2$ | $11$ |
280.384.11-280.kk.2.3 | $280$ | $2$ | $2$ | $11$ |
280.384.11-280.kk.2.12 | $280$ | $2$ | $2$ | $11$ |
280.384.11-280.kl.1.4 | $280$ | $2$ | $2$ | $11$ |
280.384.11-280.kl.1.10 | $280$ | $2$ | $2$ | $11$ |
280.384.11-280.kl.2.4 | $280$ | $2$ | $2$ | $11$ |
280.384.11-280.kl.2.10 | $280$ | $2$ | $2$ | $11$ |
280.384.11-280.mg.1.10 | $280$ | $2$ | $2$ | $11$ |
280.384.11-280.mg.1.13 | $280$ | $2$ | $2$ | $11$ |
280.384.11-280.mg.2.10 | $280$ | $2$ | $2$ | $11$ |
280.384.11-280.mg.2.13 | $280$ | $2$ | $2$ | $11$ |
280.384.11-280.mh.1.9 | $280$ | $2$ | $2$ | $11$ |
280.384.11-280.mh.1.14 | $280$ | $2$ | $2$ | $11$ |
280.384.11-280.mh.2.9 | $280$ | $2$ | $2$ | $11$ |
280.384.11-280.mh.2.14 | $280$ | $2$ | $2$ | $11$ |