Invariants
Level: | $280$ | $\SL_2$-level: | $40$ | Newform level: | $1$ | ||
Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
Genus: | $7 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $10^{4}\cdot20^{4}$ | Cusp orbits | $4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 12$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 7$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 20C7 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}3&236\\206&25\end{bmatrix}$, $\begin{bmatrix}5&47\\88&145\end{bmatrix}$, $\begin{bmatrix}9&248\\30&271\end{bmatrix}$, $\begin{bmatrix}257&181\\268&13\end{bmatrix}$, $\begin{bmatrix}257&234\\40&233\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 140.120.7.u.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $192$ |
Cyclic 280-torsion field degree: | $9216$ |
Full 280-torsion field degree: | $6193152$ |
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 |
---|---|---|---|---|---|
40.120.3-20.b.1.3 | $40$ | $2$ | $2$ | $3$ | $0$ |
280.24.0-140.e.1.4 | $280$ | $10$ | $10$ | $0$ | $?$ |
280.120.3-20.b.1.7 | $280$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
280.480.13-140.ey.1.6 | $280$ | $2$ | $2$ | $13$ |
280.480.13-140.fa.1.2 | $280$ | $2$ | $2$ | $13$ |
280.480.13-140.fg.1.4 | $280$ | $2$ | $2$ | $13$ |
280.480.13-140.fi.1.3 | $280$ | $2$ | $2$ | $13$ |
280.480.13-140.ge.1.4 | $280$ | $2$ | $2$ | $13$ |
280.480.13-140.gg.1.4 | $280$ | $2$ | $2$ | $13$ |
280.480.13-140.gm.1.4 | $280$ | $2$ | $2$ | $13$ |
280.480.13-140.go.1.4 | $280$ | $2$ | $2$ | $13$ |
280.480.13-280.bin.1.4 | $280$ | $2$ | $2$ | $13$ |
280.480.13-280.bjb.1.4 | $280$ | $2$ | $2$ | $13$ |
280.480.13-280.bkr.1.7 | $280$ | $2$ | $2$ | $13$ |
280.480.13-280.blf.1.7 | $280$ | $2$ | $2$ | $13$ |
280.480.13-280.bym.1.2 | $280$ | $2$ | $2$ | $13$ |
280.480.13-280.bza.1.2 | $280$ | $2$ | $2$ | $13$ |
280.480.13-280.caq.1.5 | $280$ | $2$ | $2$ | $13$ |
280.480.13-280.cbe.1.5 | $280$ | $2$ | $2$ | $13$ |