Modular curve 264.48.1.dg.1

• Label: 264.48.1.dg.1
• Level: $264$
• Index: $48$
• Genus: $1$
• Cusps: $8$
• $\Q$-cusps: $4$

Invariants

Level:	$264$		$\SL_2$-level:	$12$		Newform level:	$1$
Index:	$48$		$\PSL_2$-index:	$48$
Genus:	$1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$
Cusps:	$8$ (of which $4$ are rational)		Cusp widths	$2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$		Cusp orbits	$1^{4}\cdot2^{2}$
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:

12P1

Level structure

$\GL_2(\Z/264\Z)$-generators:	$\begin{bmatrix}53&186\\174&59\end{bmatrix}$, $\begin{bmatrix}61&122\\48&89\end{bmatrix}$, $\begin{bmatrix}75&140\\122&129\end{bmatrix}$, $\begin{bmatrix}107&46\\30&235\end{bmatrix}$, $\begin{bmatrix}133&68\\162&119\end{bmatrix}$, $\begin{bmatrix}229&246\\174&121\end{bmatrix}$, $\begin{bmatrix}251&216\\6&71\end{bmatrix}$
Contains $-I$:	yes
Quadratic refinements:	264.96.1-264.dg.1.1, 264.96.1-264.dg.1.2, 264.96.1-264.dg.1.3, 264.96.1-264.dg.1.4, 264.96.1-264.dg.1.5, 264.96.1-264.dg.1.6, 264.96.1-264.dg.1.7, 264.96.1-264.dg.1.8, 264.96.1-264.dg.1.9, 264.96.1-264.dg.1.10, 264.96.1-264.dg.1.11, 264.96.1-264.dg.1.12, 264.96.1-264.dg.1.13, 264.96.1-264.dg.1.14, 264.96.1-264.dg.1.15, 264.96.1-264.dg.1.16, 264.96.1-264.dg.1.17, 264.96.1-264.dg.1.18, 264.96.1-264.dg.1.19, 264.96.1-264.dg.1.20, 264.96.1-264.dg.1.21, 264.96.1-264.dg.1.22, 264.96.1-264.dg.1.23, 264.96.1-264.dg.1.24, 264.96.1-264.dg.1.25, 264.96.1-264.dg.1.26, 264.96.1-264.dg.1.27, 264.96.1-264.dg.1.28, 264.96.1-264.dg.1.29, 264.96.1-264.dg.1.30, 264.96.1-264.dg.1.31, 264.96.1-264.dg.1.32, 264.96.1-264.dg.1.33, 264.96.1-264.dg.1.34, 264.96.1-264.dg.1.35, 264.96.1-264.dg.1.36, 264.96.1-264.dg.1.37, 264.96.1-264.dg.1.38, 264.96.1-264.dg.1.39, 264.96.1-264.dg.1.40
Cyclic 264-isogeny field degree:	$48$
Cyclic 264-torsion field degree:	$3840$
Full 264-torsion field degree:	$20275200$

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
$X_0(3)$	$3$	$12$	$12$	$0$	$0$	full Jacobian
88.12.0.a.1	$88$	$4$	$4$	$0$	$?$	full Jacobian

This modular curve minimally covers the modular curves listed below.

Covered curve	Level	Index	Degree	Genus	Rank	Kernel decomposition
$X_{\pm1}(2,6)$	$6$	$2$	$2$	$0$	$0$	full Jacobian
88.12.0.a.1	$88$	$4$	$4$	$0$	$?$	full Jacobian
264.24.0.fi.1	$264$	$2$	$2$	$0$	$?$	full Jacobian
264.24.1.hn.1	$264$	$2$	$2$	$1$	$?$	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
264.96.1.lm.1	$264$	$2$	$2$	$1$	$?$	dimension zero
264.96.1.lm.2	$264$	$2$	$2$	$1$	$?$	dimension zero
264.96.1.lm.3	$264$	$2$	$2$	$1$	$?$	dimension zero
264.96.1.lm.4	$264$	$2$	$2$	$1$	$?$	dimension zero
264.96.1.lo.1	$264$	$2$	$2$	$1$	$?$	dimension zero
264.96.1.lo.2	$264$	$2$	$2$	$1$	$?$	dimension zero
264.96.1.lo.3	$264$	$2$	$2$	$1$	$?$	dimension zero
264.96.1.lo.4	$264$	$2$	$2$	$1$	$?$	dimension zero
264.96.3.cq.1	$264$	$2$	$2$	$3$	$?$	not computed
264.96.3.cr.1	$264$	$2$	$2$	$3$	$?$	not computed
264.96.3.cu.1	$264$	$2$	$2$	$3$	$?$	not computed
264.96.3.cw.1	$264$	$2$	$2$	$3$	$?$	not computed
264.96.3.de.1	$264$	$2$	$2$	$3$	$?$	not computed
264.96.3.dg.1	$264$	$2$	$2$	$3$	$?$	not computed
264.96.3.dk.1	$264$	$2$	$2$	$3$	$?$	not computed
264.96.3.dm.1	$264$	$2$	$2$	$3$	$?$	not computed
264.96.3.em.1	$264$	$2$	$2$	$3$	$?$	not computed
264.96.3.em.2	$264$	$2$	$2$	$3$	$?$	not computed
264.96.3.eo.1	$264$	$2$	$2$	$3$	$?$	not computed
264.96.3.eo.2	$264$	$2$	$2$	$3$	$?$	not computed
264.96.3.fh.1	$264$	$2$	$2$	$3$	$?$	not computed
264.96.3.fh.2	$264$	$2$	$2$	$3$	$?$	not computed
264.96.3.fi.1	$264$	$2$	$2$	$3$	$?$	not computed
264.96.3.fi.2	$264$	$2$	$2$	$3$	$?$	not computed
264.144.5.a.1	$264$	$3$	$3$	$5$	$?$	not computed