Invariants
| Level: | $280$ | $\SL_2$-level: | $8$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| 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: | 8G0 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}37&208\\55&103\end{bmatrix}$, $\begin{bmatrix}81&128\\161&85\end{bmatrix}$, $\begin{bmatrix}109&72\\147&237\end{bmatrix}$, $\begin{bmatrix}179&120\\127&67\end{bmatrix}$, $\begin{bmatrix}205&104\\86&189\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 280.24.0.dh.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $48$ |
| Cyclic 280-torsion field degree: | $4608$ |
| Full 280-torsion field degree: | $30965760$ |
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 |
|---|---|---|---|---|---|
| 40.24.0-8.n.1.6 | $40$ | $2$ | $2$ | $0$ | $0$ |
| 56.24.0-8.n.1.12 | $56$ | $2$ | $2$ | $0$ | $0$ |
| 280.24.0-140.h.1.2 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.24.0-140.h.1.11 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.24.0-280.z.1.2 | $280$ | $2$ | $2$ | $0$ | $?$ |
| 280.24.0-280.z.1.20 | $280$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 280.96.0-280.ee.1.3 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.ee.2.6 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.ef.1.2 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.ef.2.7 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.eg.1.4 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.eg.2.5 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.eh.1.4 | $280$ | $2$ | $2$ | $0$ |
| 280.96.0-280.eh.2.2 | $280$ | $2$ | $2$ | $0$ |
| 280.240.8-280.fb.1.6 | $280$ | $5$ | $5$ | $8$ |
| 280.288.7-280.jc.1.11 | $280$ | $6$ | $6$ | $7$ |
| 280.384.11-280.lf.1.7 | $280$ | $8$ | $8$ | $11$ |
| 280.480.15-280.lt.1.37 | $280$ | $10$ | $10$ | $15$ |