Invariants
Level: | $280$ | $\SL_2$-level: | $56$ | Newform level: | $1$ | ||
Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $11 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $2^{4}\cdot8^{2}\cdot14^{4}\cdot56^{2}$ | Cusp orbits | $2^{6}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $5 \le \gamma \le 20$ | ||||||
$\overline{\Q}$-gonality: | $5 \le \gamma \le 11$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 56M11 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}9&224\\210&163\end{bmatrix}$, $\begin{bmatrix}33&140\\127&141\end{bmatrix}$, $\begin{bmatrix}79&56\\231&171\end{bmatrix}$, $\begin{bmatrix}183&84\\80&241\end{bmatrix}$, $\begin{bmatrix}271&252\\250&99\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.192.11.il.1 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $12$ |
Cyclic 280-torsion field degree: | $1152$ |
Full 280-torsion field degree: | $3870720$ |
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 |
---|---|---|---|---|---|
$X_0(7)$ | $7$ | $48$ | $24$ | $0$ | $0$ |
40.48.0-40.bx.1.2 | $40$ | $8$ | $8$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
40.48.0-40.bx.1.2 | $40$ | $8$ | $8$ | $0$ | $0$ |
56.192.5-56.br.1.31 | $56$ | $2$ | $2$ | $5$ | $1$ |
280.192.5-140.l.1.6 | $280$ | $2$ | $2$ | $5$ | $?$ |
280.192.5-140.l.1.18 | $280$ | $2$ | $2$ | $5$ | $?$ |
280.192.5-56.br.1.6 | $280$ | $2$ | $2$ | $5$ | $?$ |
280.192.5-280.cd.1.10 | $280$ | $2$ | $2$ | $5$ | $?$ |
280.192.5-280.cd.1.47 | $280$ | $2$ | $2$ | $5$ | $?$ |