Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{2}$ | Cusp orbits | $2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8N0 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}53&14\\60&109\end{bmatrix}$, $\begin{bmatrix}65&142\\104&205\end{bmatrix}$, $\begin{bmatrix}155&2\\176&97\end{bmatrix}$, $\begin{bmatrix}233&216\\88&83\end{bmatrix}$, $\begin{bmatrix}271&62\\104&97\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.48.0.bi.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $96$ |
Cyclic 280-torsion field degree: | $9216$ |
Full 280-torsion field degree: | $15482880$ |
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 |
---|---|---|---|---|---|
40.48.0-8.d.2.8 | $40$ | $2$ | $2$ | $0$ | $0$ |
56.48.0-8.d.2.13 | $56$ | $2$ | $2$ | $0$ | $0$ |
280.48.0-280.e.1.12 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.e.1.33 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.u.2.27 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.48.0-280.u.2.38 | $280$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
280.192.1-280.d.2.5 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ce.2.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ei.2.12 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.eq.2.11 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.id.2.5 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.il.2.7 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.jy.2.15 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.kg.2.11 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.lf.2.2 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ln.2.4 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.na.2.12 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.ni.2.10 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.oh.2.3 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.op.2.6 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.pe.2.14 | $280$ | $2$ | $2$ | $1$ |
280.192.1-280.pi.2.11 | $280$ | $2$ | $2$ | $1$ |
280.480.16-280.bw.1.15 | $280$ | $5$ | $5$ | $16$ |