Modular curve 208.24.0.m.2

• Label: 208.24.0.m.2
• Level: $208$
• Index: $24$
• Genus: $0$
• Cusps: $6$
• $\Q$-cusps: $2$

Invariants

Level:	$208$		$\SL_2$-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

$\GL_2(\Z/208\Z)$-generators:	$\begin{bmatrix}22&25\\91&172\end{bmatrix}$, $\begin{bmatrix}75&110\\8&169\end{bmatrix}$, $\begin{bmatrix}148&115\\37&106\end{bmatrix}$, $\begin{bmatrix}161&78\\146&101\end{bmatrix}$, $\begin{bmatrix}165&12\\54&75\end{bmatrix}$, $\begin{bmatrix}166&151\\205&48\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	208.48.0-208.m.2.1, 208.48.0-208.m.2.2, 208.48.0-208.m.2.3, 208.48.0-208.m.2.4, 208.48.0-208.m.2.5, 208.48.0-208.m.2.6, 208.48.0-208.m.2.7, 208.48.0-208.m.2.8, 208.48.0-208.m.2.9, 208.48.0-208.m.2.10, 208.48.0-208.m.2.11, 208.48.0-208.m.2.12, 208.48.0-208.m.2.13, 208.48.0-208.m.2.14, 208.48.0-208.m.2.15, 208.48.0-208.m.2.16, 208.48.0-208.m.2.17, 208.48.0-208.m.2.18, 208.48.0-208.m.2.19, 208.48.0-208.m.2.20, 208.48.0-208.m.2.21, 208.48.0-208.m.2.22, 208.48.0-208.m.2.23, 208.48.0-208.m.2.24, 208.48.0-208.m.2.25, 208.48.0-208.m.2.26, 208.48.0-208.m.2.27, 208.48.0-208.m.2.28, 208.48.0-208.m.2.29, 208.48.0-208.m.2.30, 208.48.0-208.m.2.31, 208.48.0-208.m.2.32
Cyclic 208-isogeny field degree:	$28$
Cyclic 208-torsion field degree:	$2688$
Full 208-torsion field degree:	$26836992$

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
208.48.0.f.2	$208$	$2$	$2$	$0$
208.48.0.g.1	$208$	$2$	$2$	$0$
208.48.0.l.1	$208$	$2$	$2$	$0$
208.48.0.n.2	$208$	$2$	$2$	$0$
208.48.0.bb.2	$208$	$2$	$2$	$0$
208.48.0.bc.1	$208$	$2$	$2$	$0$
208.48.0.be.1	$208$	$2$	$2$	$0$
208.48.0.bh.2	$208$	$2$	$2$	$0$
208.48.0.bm.2	$208$	$2$	$2$	$0$
208.48.0.bn.2	$208$	$2$	$2$	$0$
208.48.0.bu.2	$208$	$2$	$2$	$0$
208.48.0.bv.2	$208$	$2$	$2$	$0$
208.48.0.ca.2	$208$	$2$	$2$	$0$
208.48.0.cb.2	$208$	$2$	$2$	$0$
208.48.0.ce.2	$208$	$2$	$2$	$0$
208.48.0.cf.2	$208$	$2$	$2$	$0$
208.48.1.bg.2	$208$	$2$	$2$	$1$
208.48.1.bh.1	$208$	$2$	$2$	$1$
208.48.1.bk.2	$208$	$2$	$2$	$1$
208.48.1.bl.2	$208$	$2$	$2$	$1$
208.48.1.bs.2	$208$	$2$	$2$	$1$
208.48.1.bt.1	$208$	$2$	$2$	$1$
208.48.1.ca.2	$208$	$2$	$2$	$1$
208.48.1.cb.2	$208$	$2$	$2$	$1$
208.336.23.bt.2	$208$	$14$	$14$	$23$