Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $8^{24}$ | Cusp orbits | $2^{2}\cdot4^{3}\cdot8$ | ||
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: | 8A5 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}29&236\\176&105\end{bmatrix}$, $\begin{bmatrix}123&188\\76&207\end{bmatrix}$, $\begin{bmatrix}141&240\\44&73\end{bmatrix}$, $\begin{bmatrix}187&238\\16&141\end{bmatrix}$, $\begin{bmatrix}277&214\\132&155\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 280.384.5-280.bo.1.1, 280.384.5-280.bo.1.2, 280.384.5-280.bo.1.3, 280.384.5-280.bo.1.4, 280.384.5-280.bo.1.5, 280.384.5-280.bo.1.6, 280.384.5-280.bo.1.7, 280.384.5-280.bo.1.8, 280.384.5-280.bo.1.9, 280.384.5-280.bo.1.10, 280.384.5-280.bo.1.11, 280.384.5-280.bo.1.12, 280.384.5-280.bo.1.13, 280.384.5-280.bo.1.14, 280.384.5-280.bo.1.15, 280.384.5-280.bo.1.16 |
Cyclic 280-isogeny field degree: | $96$ |
Cyclic 280-torsion field degree: | $9216$ |
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 |
---|---|---|---|---|---|
40.96.1.h.1 | $40$ | $2$ | $2$ | $1$ | $1$ |
56.96.1.n.2 | $56$ | $2$ | $2$ | $1$ | $1$ |
280.96.1.h.1 | $280$ | $2$ | $2$ | $1$ | $?$ |
280.96.3.t.1 | $280$ | $2$ | $2$ | $3$ | $?$ |
280.96.3.bw.3 | $280$ | $2$ | $2$ | $3$ | $?$ |
280.96.3.bz.1 | $280$ | $2$ | $2$ | $3$ | $?$ |
280.96.3.cf.2 | $280$ | $2$ | $2$ | $3$ | $?$ |