Modular curve 84.24.1.o.1

• Label: 84.24.1.o.1
• Level: $84$
• Index: $24$
• Genus: $1$
• Cusps: $4$
• $\Q$-cusps: $4$

Invariants

Level:	$84$		$\SL_2$-level:	$12$		Newform level:	$1$
Index:	$24$		$\PSL_2$-index:	$24$
Genus:	$1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$
Cusps:	$4$ (all of which are rational)		Cusp widths	$2\cdot4\cdot6\cdot12$		Cusp orbits	$1^{4}$
Elliptic points:	$0$ of order $2$ and $0$ of order $3$
Analytic rank:	not computed
$\Q$-gonality:	$2$
$\overline{\Q}$-gonality:	$2$
Rational cusps:	$4$
Rational CM points:	none

Other labels

Cummins and Pauli (CP) label:

12F1

Level structure

$\GL_2(\Z/84\Z)$-generators:	$\begin{bmatrix}5&42\\0&65\end{bmatrix}$, $\begin{bmatrix}6&47\\19&20\end{bmatrix}$, $\begin{bmatrix}22&59\\51&80\end{bmatrix}$, $\begin{bmatrix}50&37\\11&0\end{bmatrix}$, $\begin{bmatrix}53&64\\60&37\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	84.48.1-84.o.1.1, 84.48.1-84.o.1.2, 84.48.1-84.o.1.3, 84.48.1-84.o.1.4, 84.48.1-84.o.1.5, 84.48.1-84.o.1.6, 84.48.1-84.o.1.7, 84.48.1-84.o.1.8, 84.48.1-84.o.1.9, 84.48.1-84.o.1.10, 84.48.1-84.o.1.11, 84.48.1-84.o.1.12, 84.48.1-84.o.1.13, 84.48.1-84.o.1.14, 84.48.1-84.o.1.15, 84.48.1-84.o.1.16, 168.48.1-84.o.1.1, 168.48.1-84.o.1.2, 168.48.1-84.o.1.3, 168.48.1-84.o.1.4, 168.48.1-84.o.1.5, 168.48.1-84.o.1.6, 168.48.1-84.o.1.7, 168.48.1-84.o.1.8, 168.48.1-84.o.1.9, 168.48.1-84.o.1.10, 168.48.1-84.o.1.11, 168.48.1-84.o.1.12, 168.48.1-84.o.1.13, 168.48.1-84.o.1.14, 168.48.1-84.o.1.15, 168.48.1-84.o.1.16
Cyclic 84-isogeny field degree:	$16$
Cyclic 84-torsion field degree:	$384$
Full 84-torsion field degree:	$387072$

Jacobian

Conductor:	$?$
Simple:	yes
Squarefree:	yes
Decomposition:	$1$
Newforms:	not computed

Rational points

This modular curve is an elliptic curve, but the rank has not been computed

Modular covers

The following modular covers realize this modular curve as a fiber product over $X(1)$.

Factor curve	Level	Index	Degree	Genus	Rank	Kernel decomposition
$X_0(3)$	$3$	$6$	$6$	$0$	$0$	full Jacobian
28.6.0.d.1	$28$	$4$	$4$	$0$	$0$	full Jacobian

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank	Kernel decomposition
$X_0(6)$	$6$	$2$	$2$	$0$	$0$	full Jacobian
28.6.0.d.1	$28$	$4$	$4$	$0$	$0$	full Jacobian

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

Covering curve	Level	Index	Degree	Genus	Rank	Kernel decomposition
84.48.1.b.1	$84$	$2$	$2$	$1$	$?$	dimension zero
84.48.1.e.1	$84$	$2$	$2$	$1$	$?$	dimension zero
84.48.1.j.1	$84$	$2$	$2$	$1$	$?$	dimension zero
84.48.1.k.1	$84$	$2$	$2$	$1$	$?$	dimension zero
84.48.1.y.1	$84$	$2$	$2$	$1$	$?$	dimension zero
84.48.1.ba.1	$84$	$2$	$2$	$1$	$?$	dimension zero
84.48.1.bc.1	$84$	$2$	$2$	$1$	$?$	dimension zero
84.48.1.be.1	$84$	$2$	$2$	$1$	$?$	dimension zero
84.72.3.ma.1	$84$	$3$	$3$	$3$	$?$	not computed
84.192.13.z.1	$84$	$8$	$8$	$13$	$?$	not computed
168.48.1.gl.1	$168$	$2$	$2$	$1$	$?$	dimension zero
168.48.1.jy.1	$168$	$2$	$2$	$1$	$?$	dimension zero
168.48.1.yz.1	$168$	$2$	$2$	$1$	$?$	dimension zero
168.48.1.zc.1	$168$	$2$	$2$	$1$	$?$	dimension zero
168.48.1.bkw.1	$168$	$2$	$2$	$1$	$?$	dimension zero
168.48.1.blc.1	$168$	$2$	$2$	$1$	$?$	dimension zero
168.48.1.bli.1	$168$	$2$	$2$	$1$	$?$	dimension zero
168.48.1.blo.1	$168$	$2$	$2$	$1$	$?$	dimension zero
252.72.3.ce.1	$252$	$3$	$3$	$3$	$?$	not computed
252.72.5.p.1	$252$	$3$	$3$	$5$	$?$	not computed
252.72.5.t.1	$252$	$3$	$3$	$5$	$?$	not computed