Modular curve 56.48.0.w.1

• Label: 56.48.0.w.1
• Level: $56$
• Index: $48$
• Genus: $0$
• Analytic rank: $0$
• Cusps: $10$
• $\Q$-cusps: $0$

Invariants

Level:	$56$		$\SL_2$-level:	$8$
Index:	$48$		$\PSL_2$-index:	$48$
Genus:	$0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$
Cusps:	$10$ (none of which are rational)		Cusp widths	$2^{4}\cdot4^{2}\cdot8^{4}$		Cusp orbits	$2^{3}\cdot4$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
$\Q$-gonality:	$1 \le \gamma \le 2$
$\overline{\Q}$-gonality:	$1$
Rational cusps:	$0$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:	8O0
Rouse, Sutherland, and Zureick-Brown (RSZB) label:	56.48.0.425

Level structure

$\GL_2(\Z/56\Z)$-generators:	$\begin{bmatrix}27&20\\6&17\end{bmatrix}$, $\begin{bmatrix}29&22\\36&35\end{bmatrix}$, $\begin{bmatrix}37&32\\16&17\end{bmatrix}$, $\begin{bmatrix}39&46\\40&25\end{bmatrix}$, $\begin{bmatrix}53&32\\24&29\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	56.96.0-56.w.1.1, 56.96.0-56.w.1.2, 56.96.0-56.w.1.3, 56.96.0-56.w.1.4, 56.96.0-56.w.1.5, 56.96.0-56.w.1.6, 56.96.0-56.w.1.7, 56.96.0-56.w.1.8, 56.96.0-56.w.1.9, 56.96.0-56.w.1.10, 56.96.0-56.w.1.11, 56.96.0-56.w.1.12, 56.96.0-56.w.1.13, 56.96.0-56.w.1.14, 56.96.0-56.w.1.15, 56.96.0-56.w.1.16, 168.96.0-56.w.1.1, 168.96.0-56.w.1.2, 168.96.0-56.w.1.3, 168.96.0-56.w.1.4, 168.96.0-56.w.1.5, 168.96.0-56.w.1.6, 168.96.0-56.w.1.7, 168.96.0-56.w.1.8, 168.96.0-56.w.1.9, 168.96.0-56.w.1.10, 168.96.0-56.w.1.11, 168.96.0-56.w.1.12, 168.96.0-56.w.1.13, 168.96.0-56.w.1.14, 168.96.0-56.w.1.15, 168.96.0-56.w.1.16, 280.96.0-56.w.1.1, 280.96.0-56.w.1.2, 280.96.0-56.w.1.3, 280.96.0-56.w.1.4, 280.96.0-56.w.1.5, 280.96.0-56.w.1.6, 280.96.0-56.w.1.7, 280.96.0-56.w.1.8, 280.96.0-56.w.1.9, 280.96.0-56.w.1.10, 280.96.0-56.w.1.11, 280.96.0-56.w.1.12, 280.96.0-56.w.1.13, 280.96.0-56.w.1.14, 280.96.0-56.w.1.15, 280.96.0-56.w.1.16
Cyclic 56-isogeny field degree:	$16$
Cyclic 56-torsion field degree:	$384$
Full 56-torsion field degree:	$64512$

Models

Smooth plane model Smooth plane model

$ 0 $

$=$

$ 8 x^{2} - 7 y^{2} - 14 z^{2} $

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

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This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
8.24.0.h.1	$8$	$2$	$2$	$0$	$0$
56.24.0.h.1	$56$	$2$	$2$	$0$	$0$
56.24.0.h.2	$56$	$2$	$2$	$0$	$0$

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

Covering curve	Level	Index	Degree	Genus
56.96.1.e.1	$56$	$2$	$2$	$1$
56.96.1.e.2	$56$	$2$	$2$	$1$
56.96.1.k.1	$56$	$2$	$2$	$1$
56.96.1.k.2	$56$	$2$	$2$	$1$
56.96.1.bu.1	$56$	$2$	$2$	$1$
56.96.1.bu.2	$56$	$2$	$2$	$1$
56.96.1.bv.1	$56$	$2$	$2$	$1$
56.96.1.bv.2	$56$	$2$	$2$	$1$
56.384.23.dd.1	$56$	$8$	$8$	$23$
56.1008.70.et.1	$56$	$21$	$21$	$70$
56.1344.93.et.1	$56$	$28$	$28$	$93$
168.96.1.ko.1	$168$	$2$	$2$	$1$
168.96.1.ko.2	$168$	$2$	$2$	$1$
168.96.1.kp.1	$168$	$2$	$2$	$1$
168.96.1.kp.2	$168$	$2$	$2$	$1$
168.96.1.pe.1	$168$	$2$	$2$	$1$
168.96.1.pe.2	$168$	$2$	$2$	$1$
168.96.1.pf.1	$168$	$2$	$2$	$1$
168.96.1.pf.2	$168$	$2$	$2$	$1$
168.144.8.oo.1	$168$	$3$	$3$	$8$
168.192.7.jg.1	$168$	$4$	$4$	$7$
280.96.1.ko.1	$280$	$2$	$2$	$1$
280.96.1.ko.2	$280$	$2$	$2$	$1$
280.96.1.kp.1	$280$	$2$	$2$	$1$
280.96.1.kp.2	$280$	$2$	$2$	$1$
280.96.1.ok.1	$280$	$2$	$2$	$1$
280.96.1.ok.2	$280$	$2$	$2$	$1$
280.96.1.ol.1	$280$	$2$	$2$	$1$
280.96.1.ol.2	$280$	$2$	$2$	$1$
280.240.16.dq.1	$280$	$5$	$5$	$16$
280.288.15.jm.1	$280$	$6$	$6$	$15$