Invariants
Level: | $280$ | $\SL_2$-level: | $40$ | 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 $4$ are rational) | Cusp widths | $2^{4}\cdot8^{2}\cdot10^{4}\cdot40^{2}$ | Cusp orbits | $1^{4}\cdot2^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 7$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 7$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 40M7 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}11&20\\104&69\end{bmatrix}$, $\begin{bmatrix}71&120\\62&131\end{bmatrix}$, $\begin{bmatrix}121&180\\17&41\end{bmatrix}$, $\begin{bmatrix}181&160\\163&263\end{bmatrix}$, $\begin{bmatrix}201&100\\10&99\end{bmatrix}$, $\begin{bmatrix}277&100\\84&171\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.144.7.je.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $8$ |
Cyclic 280-torsion field degree: | $768$ |
Full 280-torsion field degree: | $5160960$ |
Rational points
This modular curve has 4 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 |
---|---|---|---|---|---|
40.144.3-40.bx.1.39 | $40$ | $2$ | $2$ | $3$ | $0$ |
280.48.0-280.dj.1.7 | $280$ | $6$ | $6$ | $0$ | $?$ |
280.144.3-40.bx.1.44 | $280$ | $2$ | $2$ | $3$ | $?$ |
280.144.3-280.cf.1.16 | $280$ | $2$ | $2$ | $3$ | $?$ |
280.144.3-280.cf.1.19 | $280$ | $2$ | $2$ | $3$ | $?$ |
280.144.3-280.ck.1.5 | $280$ | $2$ | $2$ | $3$ | $?$ |
280.144.3-280.ck.1.22 | $280$ | $2$ | $2$ | $3$ | $?$ |