Invariants
Level: | $280$ | $\SL_2$-level: | $28$ | Newform level: | $1$ | ||
Index: | $504$ | $\PSL_2$-index: | $252$ | ||||
Genus: | $16 = 1 + \frac{ 252 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $14^{6}\cdot28^{6}$ | Cusp orbits | $3^{2}\cdot6$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $5 \le \gamma \le 30$ | ||||||
$\overline{\Q}$-gonality: | $5 \le \gamma \le 16$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 28C16 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}11&40\\80&269\end{bmatrix}$, $\begin{bmatrix}57&114\\42&55\end{bmatrix}$, $\begin{bmatrix}93&22\\30&251\end{bmatrix}$, $\begin{bmatrix}157&250\\248&23\end{bmatrix}$, $\begin{bmatrix}191&68\\80&211\end{bmatrix}$, $\begin{bmatrix}273&4\\162&107\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 140.252.16.b.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $192$ |
Cyclic 280-torsion field degree: | $18432$ |
Full 280-torsion field degree: | $2949120$ |
Rational points
This modular curve has no $\Q_p$ points for $p=11$, and therefore no 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 |
---|---|---|---|---|---|
$X_{\mathrm{ns}}^+(7)$ | $7$ | $24$ | $12$ | $0$ | $0$ |
40.24.0-20.b.1.2 | $40$ | $21$ | $21$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
40.24.0-20.b.1.2 | $40$ | $21$ | $21$ | $0$ | $0$ |
56.252.7-14.a.1.4 | $56$ | $2$ | $2$ | $7$ | $0$ |
280.252.7-14.a.1.4 | $280$ | $2$ | $2$ | $7$ | $?$ |