Invariants
Level: | $280$ | $\SL_2$-level: | $4$ | ||||
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 | $4^{6}$ | 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: | 4G0 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}71&76\\4&117\end{bmatrix}$, $\begin{bmatrix}93&82\\60&121\end{bmatrix}$, $\begin{bmatrix}101&96\\24&27\end{bmatrix}$, $\begin{bmatrix}183&228\\188&247\end{bmatrix}$, $\begin{bmatrix}247&136\\40&231\end{bmatrix}$, $\begin{bmatrix}259&218\\8&9\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.24.0.e.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $96$ |
Cyclic 280-torsion field degree: | $9216$ |
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 |
---|---|---|---|---|---|
28.24.0-4.b.1.2 | $28$ | $2$ | $2$ | $0$ | $0$ |
40.24.0-4.b.1.11 | $40$ | $2$ | $2$ | $0$ | $0$ |
280.24.0-280.a.1.7 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.24.0-280.a.1.15 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.24.0-280.b.1.3 | $280$ | $2$ | $2$ | $0$ | $?$ |
280.24.0-280.b.1.12 | $280$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.