Modular curve 48.96.1.ec.1

• Label: 48.96.1.ec.1
• Level: $48$
• Index: $96$
• Genus: $1$
• Analytic rank: $0$
• Cusps: $16$
• $\Q$-cusps: $4$

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 $4$ are rational)		Cusp widths	$2^{8}\cdot4^{4}\cdot16^{4}$		Cusp orbits	$1^{4}\cdot4^{3}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	$0$
$\Q$-gonality:	$2$
$\overline{\Q}$-gonality:	$2$
Rational cusps:	$4$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:	16M1
Rouse, Sutherland, and Zureick-Brown (RSZB) label:	48.96.1.958

Level structure

$\GL_2(\Z/48\Z)$-generators:	$\begin{bmatrix}15&16\\32&7\end{bmatrix}$, $\begin{bmatrix}25&23\\28&25\end{bmatrix}$, $\begin{bmatrix}33&14\\44&43\end{bmatrix}$, $\begin{bmatrix}39&40\\32&47\end{bmatrix}$, $\begin{bmatrix}45&40\\8&41\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	48.192.1-48.ec.1.1, 48.192.1-48.ec.1.2, 48.192.1-48.ec.1.3, 48.192.1-48.ec.1.4, 48.192.1-48.ec.1.5, 48.192.1-48.ec.1.6, 48.192.1-48.ec.1.7, 48.192.1-48.ec.1.8, 48.192.1-48.ec.1.9, 48.192.1-48.ec.1.10, 48.192.1-48.ec.1.11, 48.192.1-48.ec.1.12, 96.192.1-48.ec.1.1, 96.192.1-48.ec.1.2, 96.192.1-48.ec.1.3, 96.192.1-48.ec.1.4, 96.192.1-48.ec.1.5, 96.192.1-48.ec.1.6, 96.192.1-48.ec.1.7, 96.192.1-48.ec.1.8, 240.192.1-48.ec.1.1, 240.192.1-48.ec.1.2, 240.192.1-48.ec.1.3, 240.192.1-48.ec.1.4, 240.192.1-48.ec.1.5, 240.192.1-48.ec.1.6, 240.192.1-48.ec.1.7, 240.192.1-48.ec.1.8, 240.192.1-48.ec.1.9, 240.192.1-48.ec.1.10, 240.192.1-48.ec.1.11, 240.192.1-48.ec.1.12
Cyclic 48-isogeny field degree:	$4$
Cyclic 48-torsion field degree:	$64$
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 4 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.v.2	$16$	$2$	$2$	$0$	$0$	full Jacobian
24.48.0.bn.1	$24$	$2$	$2$	$0$	$0$	full Jacobian
48.48.0.y.1	$48$	$2$	$2$	$0$	$0$	full Jacobian
48.48.0.bs.2	$48$	$2$	$2$	$0$	$0$	full Jacobian
48.48.1.bw.2	$48$	$2$	$2$	$1$	$0$	dimension zero
48.48.1.bz.2	$48$	$2$	$2$	$1$	$0$	dimension zero
48.48.1.ci.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.js.1	$48$	$2$	$2$	$5$	$0$	$2^{2}$
48.192.5.jt.1	$48$	$2$	$2$	$5$	$0$	$2^{2}$
48.192.5.ju.1	$48$	$2$	$2$	$5$	$0$	$2^{2}$
48.192.5.jv.1	$48$	$2$	$2$	$5$	$0$	$2^{2}$
48.288.17.ckz.2	$48$	$3$	$3$	$17$	$1$	$1^{8}\cdot2^{4}$
48.384.17.bma.2	$48$	$4$	$4$	$17$	$1$	$1^{8}\cdot2^{4}$
96.192.5.do.1	$96$	$2$	$2$	$5$	$?$	not computed
96.192.5.dw.1	$96$	$2$	$2$	$5$	$?$	not computed
96.192.5.ex.2	$96$	$2$	$2$	$5$	$?$	not computed
96.192.5.ey.1	$96$	$2$	$2$	$5$	$?$	not computed
96.192.5.ff.1	$96$	$2$	$2$	$5$	$?$	not computed
96.192.5.fg.1	$96$	$2$	$2$	$5$	$?$	not computed
96.192.5.ga.1	$96$	$2$	$2$	$5$	$?$	not computed
96.192.5.gi.1	$96$	$2$	$2$	$5$	$?$	not computed
240.192.5.cim.1	$240$	$2$	$2$	$5$	$?$	not computed
240.192.5.cin.1	$240$	$2$	$2$	$5$	$?$	not computed
240.192.5.cio.1	$240$	$2$	$2$	$5$	$?$	not computed
240.192.5.cip.1	$240$	$2$	$2$	$5$	$?$	not computed