Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8F1 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}13&172\\42&1\end{bmatrix}$, $\begin{bmatrix}97&226\\56&251\end{bmatrix}$, $\begin{bmatrix}143&220\\20&7\end{bmatrix}$, $\begin{bmatrix}153&174\\178&175\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.48.1.cx.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $192$ |
Cyclic 280-torsion field degree: | $18432$ |
Full 280-torsion field degree: | $15482880$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
40.48.0-40.c.1.8 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
56.48.0-56.k.1.6 | $56$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
280.48.0-40.c.1.6 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.0-56.k.1.3 | $280$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
280.48.1-280.b.1.10 | $280$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
280.48.1-280.b.1.13 | $280$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
280.480.17-280.dz.1.8 | $280$ | $5$ | $5$ | $17$ | $?$ | not computed |