Modular curve 56.48.0.o.1

• Label: 56.48.0.o.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:	56.48.0.278

Level structure

$\GL_2(\Z/56\Z)$-generators:	$\begin{bmatrix}1&8\\38&37\end{bmatrix}$, $\begin{bmatrix}3&20\\30&33\end{bmatrix}$, $\begin{bmatrix}5&52\\18&31\end{bmatrix}$, $\begin{bmatrix}9&12\\14&33\end{bmatrix}$, $\begin{bmatrix}13&8\\4&49\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	56.96.0-56.o.1.1, 56.96.0-56.o.1.2, 56.96.0-56.o.1.3, 56.96.0-56.o.1.4, 56.96.0-56.o.1.5, 56.96.0-56.o.1.6, 56.96.0-56.o.1.7, 56.96.0-56.o.1.8, 56.96.0-56.o.1.9, 56.96.0-56.o.1.10, 56.96.0-56.o.1.11, 56.96.0-56.o.1.12, 56.96.0-56.o.1.13, 56.96.0-56.o.1.14, 56.96.0-56.o.1.15, 56.96.0-56.o.1.16, 168.96.0-56.o.1.1, 168.96.0-56.o.1.2, 168.96.0-56.o.1.3, 168.96.0-56.o.1.4, 168.96.0-56.o.1.5, 168.96.0-56.o.1.6, 168.96.0-56.o.1.7, 168.96.0-56.o.1.8, 168.96.0-56.o.1.9, 168.96.0-56.o.1.10, 168.96.0-56.o.1.11, 168.96.0-56.o.1.12, 168.96.0-56.o.1.13, 168.96.0-56.o.1.14, 168.96.0-56.o.1.15, 168.96.0-56.o.1.16, 280.96.0-56.o.1.1, 280.96.0-56.o.1.2, 280.96.0-56.o.1.3, 280.96.0-56.o.1.4, 280.96.0-56.o.1.5, 280.96.0-56.o.1.6, 280.96.0-56.o.1.7, 280.96.0-56.o.1.8, 280.96.0-56.o.1.9, 280.96.0-56.o.1.10, 280.96.0-56.o.1.11, 280.96.0-56.o.1.12, 280.96.0-56.o.1.13, 280.96.0-56.o.1.14, 280.96.0-56.o.1.15, 280.96.0-56.o.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 $

$=$

$ 14 x^{2} + 56 y^{2} - 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.d.1	$8$	$2$	$2$	$0$	$0$
56.24.0.h.1	$56$	$2$	$2$	$0$	$0$
56.24.0.l.1	$56$	$2$	$2$	$0$	$0$

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

Covering curve	Level	Index	Degree	Genus
56.96.1.a.1	$56$	$2$	$2$	$1$
56.96.1.d.1	$56$	$2$	$2$	$1$
56.96.1.g.1	$56$	$2$	$2$	$1$
56.96.1.j.1	$56$	$2$	$2$	$1$
56.96.1.ba.1	$56$	$2$	$2$	$1$
56.96.1.bb.1	$56$	$2$	$2$	$1$
56.96.1.bc.1	$56$	$2$	$2$	$1$
56.96.1.bd.1	$56$	$2$	$2$	$1$
56.384.23.co.1	$56$	$8$	$8$	$23$
56.1008.70.ec.2	$56$	$21$	$21$	$70$
56.1344.93.ec.1	$56$	$28$	$28$	$93$
168.96.1.ic.2	$168$	$2$	$2$	$1$
168.96.1.id.2	$168$	$2$	$2$	$1$
168.96.1.ig.1	$168$	$2$	$2$	$1$
168.96.1.ih.1	$168$	$2$	$2$	$1$
168.96.1.ji.1	$168$	$2$	$2$	$1$
168.96.1.jj.1	$168$	$2$	$2$	$1$
168.96.1.jm.2	$168$	$2$	$2$	$1$
168.96.1.jn.2	$168$	$2$	$2$	$1$
168.144.8.ms.2	$168$	$3$	$3$	$8$
168.192.7.hg.2	$168$	$4$	$4$	$7$
280.96.1.ic.1	$280$	$2$	$2$	$1$
280.96.1.id.1	$280$	$2$	$2$	$1$
280.96.1.ig.2	$280$	$2$	$2$	$1$
280.96.1.ih.2	$280$	$2$	$2$	$1$
280.96.1.ji.2	$280$	$2$	$2$	$1$
280.96.1.jj.2	$280$	$2$	$2$	$1$
280.96.1.jm.1	$280$	$2$	$2$	$1$
280.96.1.jn.1	$280$	$2$	$2$	$1$
280.240.16.cs.2	$280$	$5$	$5$	$16$
280.288.15.hg.1	$280$	$6$	$6$	$15$