Invariants
| Level: | $280$ | $\SL_2$-level: | $280$ | Newform level: | $1$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $18 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $5^{2}\cdot20\cdot35^{2}\cdot140$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $5 \le \gamma \le 18$ | ||||||
| $\overline{\Q}$-gonality: | $5 \le \gamma \le 18$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 140A18 |
Level structure
| $\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}113&68\\160&147\end{bmatrix}$, $\begin{bmatrix}172&109\\55&254\end{bmatrix}$, $\begin{bmatrix}233&136\\168&33\end{bmatrix}$, $\begin{bmatrix}249&228\\264&269\end{bmatrix}$, $\begin{bmatrix}251&210\\190&61\end{bmatrix}$, $\begin{bmatrix}261&2\\218&269\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 140.240.18.b.1 for the level structure with $-I$) |
| Cyclic 280-isogeny field degree: | $24$ |
| Cyclic 280-torsion field degree: | $2304$ |
| Full 280-torsion field degree: | $3096576$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_0(7)$ | $7$ | $60$ | $30$ | $0$ | $0$ |
| 40.60.2-20.b.1.6 | $40$ | $8$ | $8$ | $2$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 40.60.2-20.b.1.6 | $40$ | $8$ | $8$ | $2$ | $0$ |
| 280.96.2-28.b.1.15 | $280$ | $5$ | $5$ | $2$ | $?$ |