Modular curve 48.96.1.q.2

• Label: 48.96.1.q.2
• Level: $48$
• Index: $96$
• Genus: $1$
• Analytic rank: $0$
• Cusps: $16$
• $\Q$-cusps: $2$

Invariants

Level:	$48$		$\SL_2$-level:	$16$		Newform level:	$288$
Index:	$96$		$\PSL_2$-index:	$96$
Genus:	$1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$
Cusps:	$16$ (of which $2$ are rational)		Cusp widths	$2^{8}\cdot4^{4}\cdot16^{4}$		Cusp orbits	$1^{2}\cdot2^{3}\cdot8$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	$0$
$\Q$-gonality:	$2$
$\overline{\Q}$-gonality:	$2$
Rational cusps:	$2$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:	16M1
Rouse, Sutherland, and Zureick-Brown (RSZB) label:	48.96.1.531

Level structure

$\GL_2(\Z/48\Z)$-generators:	$\begin{bmatrix}9&44\\16&19\end{bmatrix}$, $\begin{bmatrix}11&0\\24&1\end{bmatrix}$, $\begin{bmatrix}25&30\\24&47\end{bmatrix}$, $\begin{bmatrix}29&30\\32&11\end{bmatrix}$, $\begin{bmatrix}31&46\\0&5\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	48.192.1-48.q.2.1, 48.192.1-48.q.2.2, 48.192.1-48.q.2.3, 48.192.1-48.q.2.4, 48.192.1-48.q.2.5, 48.192.1-48.q.2.6, 48.192.1-48.q.2.7, 48.192.1-48.q.2.8, 48.192.1-48.q.2.9, 48.192.1-48.q.2.10, 48.192.1-48.q.2.11, 48.192.1-48.q.2.12, 48.192.1-48.q.2.13, 48.192.1-48.q.2.14, 48.192.1-48.q.2.15, 48.192.1-48.q.2.16, 240.192.1-48.q.2.1, 240.192.1-48.q.2.2, 240.192.1-48.q.2.3, 240.192.1-48.q.2.4, 240.192.1-48.q.2.5, 240.192.1-48.q.2.6, 240.192.1-48.q.2.7, 240.192.1-48.q.2.8, 240.192.1-48.q.2.9, 240.192.1-48.q.2.10, 240.192.1-48.q.2.11, 240.192.1-48.q.2.12, 240.192.1-48.q.2.13, 240.192.1-48.q.2.14, 240.192.1-48.q.2.15, 240.192.1-48.q.2.16
Cyclic 48-isogeny field degree:	$8$
Cyclic 48-torsion field degree:	$128$
Full 48-torsion field degree:	$12288$

Jacobian

Conductor:	$2^{5}\cdot3^{2}$
Simple:	yes
Squarefree:	yes
Decomposition:	$1$
Newforms:	288.2.a.d

Rational points

This modular curve has 2 rational cusps but no known non-cuspidal 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	Kernel decomposition
16.48.0.d.1	$16$	$2$	$2$	$0$	$0$	full Jacobian
24.48.0.bb.2	$24$	$2$	$2$	$0$	$0$	full Jacobian
48.48.1.b.1	$48$	$2$	$2$	$1$	$0$	dimension zero

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

Covering curve	Level	Index	Degree	Genus	Rank	Kernel decomposition
48.192.5.z.2	$48$	$2$	$2$	$5$	$1$	$1^{2}\cdot2$
48.192.5.bh.3	$48$	$2$	$2$	$5$	$1$	$1^{2}\cdot2$
48.192.5.cg.2	$48$	$2$	$2$	$5$	$0$	$1^{2}\cdot2$
48.192.5.ci.2	$48$	$2$	$2$	$5$	$0$	$1^{2}\cdot2$
48.192.5.dz.1	$48$	$2$	$2$	$5$	$0$	$1^{2}\cdot2$
48.192.5.ef.2	$48$	$2$	$2$	$5$	$0$	$1^{2}\cdot2$
48.192.5.el.1	$48$	$2$	$2$	$5$	$1$	$1^{2}\cdot2$
48.192.5.eo.1	$48$	$2$	$2$	$5$	$1$	$1^{2}\cdot2$
48.288.17.ex.1	$48$	$3$	$3$	$17$	$1$	$1^{8}\cdot2^{4}$
48.384.17.io.1	$48$	$4$	$4$	$17$	$1$	$1^{8}\cdot2^{4}$
240.192.5.bfy.2	$240$	$2$	$2$	$5$	$?$	not computed
240.192.5.bfz.1	$240$	$2$	$2$	$5$	$?$	not computed
240.192.5.bgc.2	$240$	$2$	$2$	$5$	$?$	not computed
240.192.5.bgd.2	$240$	$2$	$2$	$5$	$?$	not computed
240.192.5.bgw.2	$240$	$2$	$2$	$5$	$?$	not computed
240.192.5.bgx.1	$240$	$2$	$2$	$5$	$?$	not computed
240.192.5.bhe.1	$240$	$2$	$2$	$5$	$?$	not computed
240.192.5.bhf.1	$240$	$2$	$2$	$5$	$?$	not computed