Invariants
Level: | $280$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
Genus: | $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (of which $6$ are rational) | Cusp widths | $4^{6}\cdot20^{6}$ | Cusp orbits | $1^{6}\cdot2^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 7$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 7$ | ||||||
Rational cusps: | $6$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 20J7 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}3&252\\186&97\end{bmatrix}$, $\begin{bmatrix}21&110\\120&211\end{bmatrix}$, $\begin{bmatrix}23&112\\210&121\end{bmatrix}$, $\begin{bmatrix}85&204\\106&237\end{bmatrix}$, $\begin{bmatrix}175&64\\12&13\end{bmatrix}$, $\begin{bmatrix}259&188\\232&223\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.144.7.a.2 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $32$ |
Cyclic 280-torsion field degree: | $768$ |
Full 280-torsion field degree: | $5160960$ |
Rational points
This modular curve has 6 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
$X_1(2,10)$ | $10$ | $2$ | $2$ | $1$ | $0$ |
280.96.3-280.a.2.1 | $280$ | $3$ | $3$ | $3$ | $?$ |
280.144.1-10.a.1.11 | $280$ | $2$ | $2$ | $1$ | $?$ |