Invariants
Level: | $280$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $8^{12}$ | Cusp orbits | $2^{4}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8B3 |
Level structure
$\GL_2(\Z/280\Z)$-generators: | $\begin{bmatrix}1&128\\76&169\end{bmatrix}$, $\begin{bmatrix}33&76\\232&85\end{bmatrix}$, $\begin{bmatrix}75&158\\244&265\end{bmatrix}$, $\begin{bmatrix}131&98\\208&57\end{bmatrix}$, $\begin{bmatrix}187&96\\20&87\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 280.96.3.cc.2 for the level structure with $-I$) |
Cyclic 280-isogeny field degree: | $96$ |
Cyclic 280-torsion field degree: | $4608$ |
Full 280-torsion field degree: | $7741440$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
40.96.0-40.b.2.10 | $40$ | $2$ | $2$ | $0$ | $0$ |
280.96.0-40.b.2.20 | $280$ | $2$ | $2$ | $0$ | $?$ |
56.96.1-56.n.2.24 | $56$ | $2$ | $2$ | $1$ | $1$ |
280.96.1-56.n.2.7 | $280$ | $2$ | $2$ | $1$ | $?$ |
280.96.2-280.a.1.16 | $280$ | $2$ | $2$ | $2$ | $?$ |
280.96.2-280.a.1.35 | $280$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
280.384.5-280.m.1.14 | $280$ | $2$ | $2$ | $5$ |
280.384.5-280.p.2.2 | $280$ | $2$ | $2$ | $5$ |
280.384.5-280.bc.2.16 | $280$ | $2$ | $2$ | $5$ |
280.384.5-280.bg.3.1 | $280$ | $2$ | $2$ | $5$ |
280.384.5-280.ck.1.13 | $280$ | $2$ | $2$ | $5$ |
280.384.5-280.cm.2.4 | $280$ | $2$ | $2$ | $5$ |
280.384.5-280.dk.1.15 | $280$ | $2$ | $2$ | $5$ |
280.384.5-280.dm.2.2 | $280$ | $2$ | $2$ | $5$ |
280.384.5-280.eq.1.2 | $280$ | $2$ | $2$ | $5$ |
280.384.5-280.es.2.15 | $280$ | $2$ | $2$ | $5$ |
280.384.5-280.fu.2.4 | $280$ | $2$ | $2$ | $5$ |
280.384.5-280.fw.2.11 | $280$ | $2$ | $2$ | $5$ |
280.384.5-280.gi.1.1 | $280$ | $2$ | $2$ | $5$ |
280.384.5-280.gm.4.16 | $280$ | $2$ | $2$ | $5$ |
280.384.5-280.hi.2.2 | $280$ | $2$ | $2$ | $5$ |
280.384.5-280.hl.2.12 | $280$ | $2$ | $2$ | $5$ |