Properties

Label 280.240.7-280.b.1.15
Level $280$
Index $240$
Genus $7$
Cusps $8$
$\Q$-cusps $0$

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Invariants

Level: $280$ $\SL_2$-level: $20$ Newform level: $1$
Index: $240$ $\PSL_2$-index:$120$
Genus: $7 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$
Cusps: $8$ (none of which are rational) Cusp widths $10^{4}\cdot20^{4}$ Cusp orbits $2^{2}\cdot4$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $4 \le \gamma \le 12$
$\overline{\Q}$-gonality: $4 \le \gamma \le 7$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 20C7

Level structure

$\GL_2(\Z/280\Z)$-generators: $\begin{bmatrix}3&180\\246&187\end{bmatrix}$, $\begin{bmatrix}41&246\\26&203\end{bmatrix}$, $\begin{bmatrix}81&228\\184&179\end{bmatrix}$, $\begin{bmatrix}89&134\\174&197\end{bmatrix}$, $\begin{bmatrix}147&76\\38&113\end{bmatrix}$, $\begin{bmatrix}269&102\\232&23\end{bmatrix}$
Contains $-I$: no $\quad$ (see 280.120.7.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: $6193152$

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
40.120.3-10.a.1.2 $40$ $2$ $2$ $3$ $0$
140.120.3-10.a.1.4 $140$ $2$ $2$ $3$ $?$
280.24.0-56.b.1.2 $280$ $10$ $10$ $0$ $?$

This modular curve is minimally covered by the modular curves in the database listed below.

Covering curve Level Index Degree Genus
280.480.13-280.d.1.16 $280$ $2$ $2$ $13$
280.480.13-280.f.1.16 $280$ $2$ $2$ $13$
280.480.13-280.j.1.8 $280$ $2$ $2$ $13$
280.480.13-280.l.1.4 $280$ $2$ $2$ $13$
280.480.13-280.bb.1.6 $280$ $2$ $2$ $13$
280.480.13-280.bd.1.11 $280$ $2$ $2$ $13$
280.480.13-280.bh.1.15 $280$ $2$ $2$ $13$
280.480.13-280.bj.1.16 $280$ $2$ $2$ $13$
280.480.13-280.ds.1.14 $280$ $2$ $2$ $13$
280.480.13-280.du.1.16 $280$ $2$ $2$ $13$
280.480.13-280.eb.1.4 $280$ $2$ $2$ $13$
280.480.13-280.ed.1.10 $280$ $2$ $2$ $13$
280.480.13-280.eq.1.8 $280$ $2$ $2$ $13$
280.480.13-280.es.1.8 $280$ $2$ $2$ $13$
280.480.13-280.ez.1.16 $280$ $2$ $2$ $13$
280.480.13-280.fb.1.16 $280$ $2$ $2$ $13$
280.480.15-280.c.1.11 $280$ $2$ $2$ $15$
280.480.15-280.c.1.17 $280$ $2$ $2$ $15$
280.480.15-280.d.1.3 $280$ $2$ $2$ $15$
280.480.15-280.d.1.15 $280$ $2$ $2$ $15$
280.480.15-280.e.1.3 $280$ $2$ $2$ $15$
280.480.15-280.e.1.21 $280$ $2$ $2$ $15$
280.480.15-280.f.1.9 $280$ $2$ $2$ $15$
280.480.15-280.f.1.31 $280$ $2$ $2$ $15$
280.480.15-280.r.1.11 $280$ $2$ $2$ $15$
280.480.15-280.r.1.15 $280$ $2$ $2$ $15$
280.480.15-280.t.1.13 $280$ $2$ $2$ $15$
280.480.15-280.t.1.15 $280$ $2$ $2$ $15$
280.480.15-280.x.1.11 $280$ $2$ $2$ $15$
280.480.15-280.x.1.13 $280$ $2$ $2$ $15$
280.480.15-280.z.1.11 $280$ $2$ $2$ $15$
280.480.15-280.z.1.13 $280$ $2$ $2$ $15$
280.480.15-280.dc.1.21 $280$ $2$ $2$ $15$
280.480.15-280.dc.1.23 $280$ $2$ $2$ $15$
280.480.15-280.dd.1.23 $280$ $2$ $2$ $15$
280.480.15-280.dd.1.31 $280$ $2$ $2$ $15$
280.480.15-280.di.1.23 $280$ $2$ $2$ $15$
280.480.15-280.di.1.27 $280$ $2$ $2$ $15$
280.480.15-280.dj.1.21 $280$ $2$ $2$ $15$
280.480.15-280.dj.1.31 $280$ $2$ $2$ $15$
280.480.15-280.do.1.23 $280$ $2$ $2$ $15$
280.480.15-280.do.1.31 $280$ $2$ $2$ $15$
280.480.15-280.dp.1.21 $280$ $2$ $2$ $15$
280.480.15-280.dp.1.23 $280$ $2$ $2$ $15$
280.480.15-280.du.1.25 $280$ $2$ $2$ $15$
280.480.15-280.du.1.31 $280$ $2$ $2$ $15$
280.480.15-280.dv.1.23 $280$ $2$ $2$ $15$
280.480.15-280.dv.1.29 $280$ $2$ $2$ $15$