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: | $\begin{bmatrix}39&64\\14&57\end{bmatrix}$, $\begin{bmatrix}71&44\\270&231\end{bmatrix}$, $\begin{bmatrix}79&68\\170&9\end{bmatrix}$, $\begin{bmatrix}83&248\\180&127\end{bmatrix}$, $\begin{bmatrix}247&124\\264&41\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.48.0.bt.2 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $96$ |
| 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 |
|---|---|---|---|---|---|
| 40.48.0-8.e.2.6 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 56.48.0-8.e.2.3 | $56$ | $2$ | $2$ | $0$ | $0$ |
| 280.48.0-280.t.2.17 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.t.2.21 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.x.1.23 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.48.0-280.x.1.25 | $280$ | $2$ | $2$ | $0$ | $?$ |
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.ba.2.3 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.bf.2.9 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.cy.2.11 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.db.2.11 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.dy.2.3 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.dz.2.5 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.eg.2.13 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.eh.2.7 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.gm.2.1 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.gn.2.1 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.gu.2.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.gv.2.14 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.hc.2.6 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.hd.2.11 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.hk.2.9 | $280$ | $2$ | $2$ | $1$ |
| 280.192.1-280.hl.2.5 | $280$ | $2$ | $2$ | $1$ |
| 280.480.16-280.ch.1.3 | $280$ | $5$ | $5$ | $16$ |