Modular curve 272.24.0.n.2

• Label: 272.24.0.n.2
• Level: $272$
• Index: $24$
• Genus: $0$
• Cusps: $6$
• $\Q$-cusps: $2$

Invariants

Level:	$272$		$\SL_2$-level:	$16$
Index:	$24$		$\PSL_2$-index:	$24$
Genus:	$0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps:	$6$ (of which $2$ are rational)		Cusp widths	$1^{2}\cdot2^{3}\cdot16$		Cusp orbits	$1^{2}\cdot2^{2}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
$\Q$-gonality:	$1$
$\overline{\Q}$-gonality:	$1$
Rational cusps:	$2$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

16D0

Level structure

$\GL_2(\Z/272\Z)$-generators:	$\begin{bmatrix}2&263\\3&102\end{bmatrix}$, $\begin{bmatrix}6&133\\211&264\end{bmatrix}$, $\begin{bmatrix}24&233\\131&174\end{bmatrix}$, $\begin{bmatrix}49&260\\242&19\end{bmatrix}$, $\begin{bmatrix}50&165\\53&122\end{bmatrix}$, $\begin{bmatrix}131&254\\220&237\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	272.48.0-272.n.2.1, 272.48.0-272.n.2.2, 272.48.0-272.n.2.3, 272.48.0-272.n.2.4, 272.48.0-272.n.2.5, 272.48.0-272.n.2.6, 272.48.0-272.n.2.7, 272.48.0-272.n.2.8, 272.48.0-272.n.2.9, 272.48.0-272.n.2.10, 272.48.0-272.n.2.11, 272.48.0-272.n.2.12, 272.48.0-272.n.2.13, 272.48.0-272.n.2.14, 272.48.0-272.n.2.15, 272.48.0-272.n.2.16, 272.48.0-272.n.2.17, 272.48.0-272.n.2.18, 272.48.0-272.n.2.19, 272.48.0-272.n.2.20, 272.48.0-272.n.2.21, 272.48.0-272.n.2.22, 272.48.0-272.n.2.23, 272.48.0-272.n.2.24, 272.48.0-272.n.2.25, 272.48.0-272.n.2.26, 272.48.0-272.n.2.27, 272.48.0-272.n.2.28, 272.48.0-272.n.2.29, 272.48.0-272.n.2.30, 272.48.0-272.n.2.31, 272.48.0-272.n.2.32
Cyclic 272-isogeny field degree:	$36$
Cyclic 272-torsion field degree:	$4608$
Full 272-torsion field degree:	$80216064$

Models

This modular curve is isomorphic to $\mathbb{P}^1$.

Rational points

This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank
$X_0(8)$	$8$	$2$	$2$	$0$	$0$

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

Covering curve	Level	Index	Degree	Genus
272.48.0.f.2	$272$	$2$	$2$	$0$
272.48.0.h.1	$272$	$2$	$2$	$0$
272.48.0.m.1	$272$	$2$	$2$	$0$
272.48.0.n.2	$272$	$2$	$2$	$0$
272.48.0.ba.1	$272$	$2$	$2$	$0$
272.48.0.bd.1	$272$	$2$	$2$	$0$
272.48.0.bf.1	$272$	$2$	$2$	$0$
272.48.0.bg.1	$272$	$2$	$2$	$0$
272.48.0.bo.1	$272$	$2$	$2$	$0$
272.48.0.bp.2	$272$	$2$	$2$	$0$
272.48.0.bw.1	$272$	$2$	$2$	$0$
272.48.0.bx.1	$272$	$2$	$2$	$0$
272.48.0.cc.1	$272$	$2$	$2$	$0$
272.48.0.cd.1	$272$	$2$	$2$	$0$
272.48.0.cg.1	$272$	$2$	$2$	$0$
272.48.0.ch.2	$272$	$2$	$2$	$0$
272.48.1.bi.1	$272$	$2$	$2$	$1$
272.48.1.bj.1	$272$	$2$	$2$	$1$
272.48.1.bm.1	$272$	$2$	$2$	$1$
272.48.1.bn.1	$272$	$2$	$2$	$1$
272.48.1.bu.1	$272$	$2$	$2$	$1$
272.48.1.bv.1	$272$	$2$	$2$	$1$
272.48.1.cc.1	$272$	$2$	$2$	$1$
272.48.1.cd.1	$272$	$2$	$2$	$1$