Modular curve 140.120.7.b.1

• Label: 140.120.7.b.1
• Level: $140$
• Index: $120$
• Genus: $7$
• Cusps: $8$
• $\Q$-cusps: $0$

Invariants

Level:	$140$		$\SL_2$-level:	$20$		Newform level:	$1$
Index:	$120$		$\PSL_2$-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

$\GL_2(\Z/140\Z)$-generators:	$\begin{bmatrix}3&16\\0&97\end{bmatrix}$, $\begin{bmatrix}19&106\\92&111\end{bmatrix}$, $\begin{bmatrix}49&124\\44&7\end{bmatrix}$, $\begin{bmatrix}75&86\\84&115\end{bmatrix}$, $\begin{bmatrix}119&36\\76&1\end{bmatrix}$, $\begin{bmatrix}127&66\\86&109\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	140.240.7-140.b.1.1, 140.240.7-140.b.1.2, 140.240.7-140.b.1.3, 140.240.7-140.b.1.4, 140.240.7-140.b.1.5, 140.240.7-140.b.1.6, 140.240.7-140.b.1.7, 140.240.7-140.b.1.8, 140.240.7-140.b.1.9, 140.240.7-140.b.1.10, 140.240.7-140.b.1.11, 140.240.7-140.b.1.12, 140.240.7-140.b.1.13, 140.240.7-140.b.1.14, 140.240.7-140.b.1.15, 140.240.7-140.b.1.16, 280.240.7-140.b.1.1, 280.240.7-140.b.1.2, 280.240.7-140.b.1.3, 280.240.7-140.b.1.4, 280.240.7-140.b.1.5, 280.240.7-140.b.1.6, 280.240.7-140.b.1.7, 280.240.7-140.b.1.8, 280.240.7-140.b.1.9, 280.240.7-140.b.1.10, 280.240.7-140.b.1.11, 280.240.7-140.b.1.12, 280.240.7-140.b.1.13, 280.240.7-140.b.1.14, 280.240.7-140.b.1.15, 280.240.7-140.b.1.16
Cyclic 140-isogeny field degree:	$96$
Cyclic 140-torsion field degree:	$4608$
Full 140-torsion field degree:	$774144$

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

The following modular covers realize this modular curve as a fiber product over $X(1)$.

Factor curve	Level	Index	Degree	Genus	Rank
$X_{\mathrm{ns}}^+(5)$	$5$	$12$	$12$	$0$	$0$
28.12.0.b.1	$28$	$10$	$10$	$0$	$0$

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
10.60.3.a.1	$10$	$2$	$2$	$3$	$0$
28.12.0.b.1	$28$	$10$	$10$	$0$	$0$
140.60.3.ba.1	$140$	$2$	$2$	$3$	$?$
140.60.3.bs.1	$140$	$2$	$2$	$3$	$?$

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

Covering curve	Level	Index	Degree	Genus
140.240.13.b.1	$140$	$2$	$2$	$13$
140.240.13.d.1	$140$	$2$	$2$	$13$
140.240.13.j.1	$140$	$2$	$2$	$13$
140.240.13.l.1	$140$	$2$	$2$	$13$
140.240.13.bg.1	$140$	$2$	$2$	$13$
140.240.13.bj.1	$140$	$2$	$2$	$13$
140.240.13.bo.1	$140$	$2$	$2$	$13$
140.240.13.br.1	$140$	$2$	$2$	$13$
140.240.15.b.1	$140$	$2$	$2$	$15$
140.240.15.c.1	$140$	$2$	$2$	$15$
140.240.15.h.1	$140$	$2$	$2$	$15$
140.240.15.j.1	$140$	$2$	$2$	$15$
140.240.15.v.1	$140$	$2$	$2$	$15$
140.240.15.x.1	$140$	$2$	$2$	$15$
140.240.15.z.1	$140$	$2$	$2$	$15$
140.240.15.bb.1	$140$	$2$	$2$	$15$
140.360.19.v.1	$140$	$3$	$3$	$19$
280.240.13.e.1	$280$	$2$	$2$	$13$
280.240.13.k.1	$280$	$2$	$2$	$13$
280.240.13.bc.1	$280$	$2$	$2$	$13$
280.240.13.bi.1	$280$	$2$	$2$	$13$
280.240.13.dt.1	$280$	$2$	$2$	$13$
280.240.13.ec.1	$280$	$2$	$2$	$13$
280.240.13.er.1	$280$	$2$	$2$	$13$
280.240.13.fa.1	$280$	$2$	$2$	$13$
280.240.15.d.1	$280$	$2$	$2$	$15$
280.240.15.g.1	$280$	$2$	$2$	$15$
280.240.15.s.1	$280$	$2$	$2$	$15$
280.240.15.y.1	$280$	$2$	$2$	$15$
280.240.15.db.1	$280$	$2$	$2$	$15$
280.240.15.dh.1	$280$	$2$	$2$	$15$
280.240.15.dn.1	$280$	$2$	$2$	$15$
280.240.15.dt.1	$280$	$2$	$2$	$15$