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: | $10$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{2}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 8O0 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}25&28\\138&51\end{bmatrix}$, $\begin{bmatrix}65&196\\96&151\end{bmatrix}$, $\begin{bmatrix}137&68\\196&143\end{bmatrix}$, $\begin{bmatrix}221&220\\20&151\end{bmatrix}$, $\begin{bmatrix}229&0\\136&213\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.48.0.cy.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $48$ |
| Cyclic 280-torsion field degree: | $4608$ |
| Full 280-torsion field degree: | $15482880$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.48.0-8.i.1.2 | $8$ | $2$ | $2$ | $0$ | $0$ |
| 280.48.0-8.i.1.7 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.t.2.4 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.t.2.6 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.u.1.4 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.u.1.8 | $280$ | $2$ | $2$ | $0$ | $?$ |
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.v.2.2 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.bu.1.4 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.fo.1.4 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.fp.2.2 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.kw.2.4 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.kz.1.3 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.la.1.3 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ld.2.4 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ny.2.4 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ob.1.3 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.oc.1.3 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.of.2.4 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.ow.2.8 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.pd.1.1 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.pe.1.1 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.pl.2.8 | $280$ | $2$ | $2$ | $1$ |
| 280.480.16-280.dy.2.25 | $280$ | $5$ | $5$ | $16$ |