Modular curve 140.252.16.t.1

• Label: 140.252.16.t.1
• Level: $140$
• Index: $252$
• Genus: $16$
• Cusps: $12$
• $\Q$-cusps: $0$

Invariants

Level:	$140$		$\SL_2$-level:	$28$		Newform level:	$1$
Index:	$252$		$\PSL_2$-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

$\GL_2(\Z/140\Z)$-generators:	$\begin{bmatrix}7&110\\4&49\end{bmatrix}$, $\begin{bmatrix}105&92\\12&49\end{bmatrix}$, $\begin{bmatrix}117&49\\28&5\end{bmatrix}$, $\begin{bmatrix}117&119\\48&65\end{bmatrix}$, $\begin{bmatrix}125&26\\28&43\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	140.504.16-140.t.1.1, 140.504.16-140.t.1.2, 140.504.16-140.t.1.3, 140.504.16-140.t.1.4, 140.504.16-140.t.1.5, 140.504.16-140.t.1.6, 140.504.16-140.t.1.7, 140.504.16-140.t.1.8, 280.504.16-140.t.1.1, 280.504.16-140.t.1.2, 280.504.16-140.t.1.3, 280.504.16-140.t.1.4, 280.504.16-140.t.1.5, 280.504.16-140.t.1.6, 280.504.16-140.t.1.7, 280.504.16-140.t.1.8, 280.504.16-140.t.1.9, 280.504.16-140.t.1.10, 280.504.16-140.t.1.11, 280.504.16-140.t.1.12, 280.504.16-140.t.1.13, 280.504.16-140.t.1.14, 280.504.16-140.t.1.15, 280.504.16-140.t.1.16, 280.504.16-140.t.1.17, 280.504.16-140.t.1.18, 280.504.16-140.t.1.19, 280.504.16-140.t.1.20, 280.504.16-140.t.1.21, 280.504.16-140.t.1.22, 280.504.16-140.t.1.23, 280.504.16-140.t.1.24
Cyclic 140-isogeny field degree:	$48$
Cyclic 140-torsion field degree:	$2304$
Full 140-torsion field degree:	$368640$

Rational points

This modular curve has no $\Q_p$ points for $p=3,67$, 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
$X_{\mathrm{ns}}^+(7)$	$7$	$12$	$12$	$0$	$0$
20.12.0.h.1	$20$	$21$	$21$	$0$	$0$

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
20.12.0.h.1	$20$	$21$	$21$	$0$	$0$
28.126.7.c.1	$28$	$2$	$2$	$7$	$0$
140.126.6.d.1	$140$	$2$	$2$	$6$	$?$
140.126.7.a.1	$140$	$2$	$2$	$7$	$?$