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Properties

Label 264.48.2.g.2
Level $264$
Index $48$
Genus $2$
Cusps $6$
$\Q$-cusps $6$

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Invariants

Level: $264$ $\SL_2$-level: $24$ Newform level: $1$
Index: $48$ $\PSL_2$-index:$48$
Genus: $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps: $6$ (all of which are rational) Cusp widths $2^{2}\cdot6^{2}\cdot8\cdot24$ Cusp orbits $1^{6}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $2$
$\overline{\Q}$-gonality: $2$
Rational cusps: $6$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 24F2

Level structure

$\GL_2(\Z/264\Z)$-generators: $\begin{bmatrix}17&112\\90&247\end{bmatrix}$, $\begin{bmatrix}79&254\\70&75\end{bmatrix}$, $\begin{bmatrix}80&157\\197&216\end{bmatrix}$, $\begin{bmatrix}85&86\\4&147\end{bmatrix}$, $\begin{bmatrix}116&253\\215&174\end{bmatrix}$, $\begin{bmatrix}158&97\\231&76\end{bmatrix}$, $\begin{bmatrix}202&251\\163&234\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 264.96.2-264.g.2.1, 264.96.2-264.g.2.2, 264.96.2-264.g.2.3, 264.96.2-264.g.2.4, 264.96.2-264.g.2.5, 264.96.2-264.g.2.6, 264.96.2-264.g.2.7, 264.96.2-264.g.2.8, 264.96.2-264.g.2.9, 264.96.2-264.g.2.10, 264.96.2-264.g.2.11, 264.96.2-264.g.2.12, 264.96.2-264.g.2.13, 264.96.2-264.g.2.14, 264.96.2-264.g.2.15, 264.96.2-264.g.2.16, 264.96.2-264.g.2.17, 264.96.2-264.g.2.18, 264.96.2-264.g.2.19, 264.96.2-264.g.2.20, 264.96.2-264.g.2.21, 264.96.2-264.g.2.22, 264.96.2-264.g.2.23, 264.96.2-264.g.2.24, 264.96.2-264.g.2.25, 264.96.2-264.g.2.26, 264.96.2-264.g.2.27, 264.96.2-264.g.2.28, 264.96.2-264.g.2.29, 264.96.2-264.g.2.30, 264.96.2-264.g.2.31, 264.96.2-264.g.2.32, 264.96.2-264.g.2.33, 264.96.2-264.g.2.34, 264.96.2-264.g.2.35, 264.96.2-264.g.2.36, 264.96.2-264.g.2.37, 264.96.2-264.g.2.38, 264.96.2-264.g.2.39, 264.96.2-264.g.2.40, 264.96.2-264.g.2.41, 264.96.2-264.g.2.42, 264.96.2-264.g.2.43, 264.96.2-264.g.2.44, 264.96.2-264.g.2.45, 264.96.2-264.g.2.46, 264.96.2-264.g.2.47, 264.96.2-264.g.2.48, 264.96.2-264.g.2.49, 264.96.2-264.g.2.50, 264.96.2-264.g.2.51, 264.96.2-264.g.2.52, 264.96.2-264.g.2.53, 264.96.2-264.g.2.54, 264.96.2-264.g.2.55, 264.96.2-264.g.2.56, 264.96.2-264.g.2.57, 264.96.2-264.g.2.58, 264.96.2-264.g.2.59, 264.96.2-264.g.2.60, 264.96.2-264.g.2.61, 264.96.2-264.g.2.62, 264.96.2-264.g.2.63, 264.96.2-264.g.2.64
Cyclic 264-isogeny field degree: $24$
Cyclic 264-torsion field degree: $1920$
Full 264-torsion field degree: $20275200$

Rational points

This modular curve has 6 rational cusps but no known non-cuspidal rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
$X_0(12)$ $12$ $2$ $2$ $0$ $0$

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

Covering curve Level Index Degree Genus
264.96.3.dt.2 $264$ $2$ $2$ $3$
264.96.3.fz.2 $264$ $2$ $2$ $3$
264.96.3.ii.2 $264$ $2$ $2$ $3$
264.96.3.il.2 $264$ $2$ $2$ $3$
264.96.3.jp.1 $264$ $2$ $2$ $3$
264.96.3.jr.1 $264$ $2$ $2$ $3$
264.96.3.kb.1 $264$ $2$ $2$ $3$
264.96.3.kd.1 $264$ $2$ $2$ $3$
264.96.3.kq.2 $264$ $2$ $2$ $3$
264.96.3.kt.1 $264$ $2$ $2$ $3$
264.96.3.ku.1 $264$ $2$ $2$ $3$
264.96.3.kx.1 $264$ $2$ $2$ $3$
264.96.3.lg.1 $264$ $2$ $2$ $3$
264.96.3.lj.2 $264$ $2$ $2$ $3$
264.96.3.lk.2 $264$ $2$ $2$ $3$
264.96.3.ln.2 $264$ $2$ $2$ $3$
264.96.3.po.3 $264$ $2$ $2$ $3$
264.96.3.po.4 $264$ $2$ $2$ $3$
264.96.3.pp.3 $264$ $2$ $2$ $3$
264.96.3.pp.4 $264$ $2$ $2$ $3$
264.96.3.ps.1 $264$ $2$ $2$ $3$
264.96.3.ps.3 $264$ $2$ $2$ $3$
264.96.3.pt.1 $264$ $2$ $2$ $3$
264.96.3.pt.3 $264$ $2$ $2$ $3$
264.96.3.pw.1 $264$ $2$ $2$ $3$
264.96.3.pw.2 $264$ $2$ $2$ $3$
264.96.3.px.1 $264$ $2$ $2$ $3$
264.96.3.px.2 $264$ $2$ $2$ $3$
264.96.3.qa.3 $264$ $2$ $2$ $3$
264.96.3.qa.4 $264$ $2$ $2$ $3$
264.96.3.qb.3 $264$ $2$ $2$ $3$
264.96.3.qb.4 $264$ $2$ $2$ $3$
264.96.3.qe.3 $264$ $2$ $2$ $3$
264.96.3.qe.4 $264$ $2$ $2$ $3$
264.96.3.qf.3 $264$ $2$ $2$ $3$
264.96.3.qf.4 $264$ $2$ $2$ $3$
264.96.3.qi.1 $264$ $2$ $2$ $3$
264.96.3.qi.2 $264$ $2$ $2$ $3$
264.96.3.qj.1 $264$ $2$ $2$ $3$
264.96.3.qj.2 $264$ $2$ $2$ $3$
264.96.3.qm.1 $264$ $2$ $2$ $3$
264.96.3.qm.3 $264$ $2$ $2$ $3$
264.96.3.qn.1 $264$ $2$ $2$ $3$
264.96.3.qn.3 $264$ $2$ $2$ $3$
264.96.3.qq.3 $264$ $2$ $2$ $3$
264.96.3.qq.4 $264$ $2$ $2$ $3$
264.96.3.qr.3 $264$ $2$ $2$ $3$
264.96.3.qr.4 $264$ $2$ $2$ $3$
264.144.7.czm.1 $264$ $3$ $3$ $7$