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Properties

Label 272.96.2.k.1
Level $272$
Index $96$
Genus $2$
Cusps $14$
$\Q$-cusps $2$

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Invariants

Level: $272$ $\SL_2$-level: $16$ Newform level: $1$
Index: $96$ $\PSL_2$-index:$96$
Genus: $2 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 14 }{2}$
Cusps: $14$ (of which $2$ are rational) Cusp widths $4^{8}\cdot8^{4}\cdot16^{2}$ Cusp orbits $1^{2}\cdot2^{4}\cdot4$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $2$
$\overline{\Q}$-gonality: $2$
Rational cusps: $2$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 16I2

Level structure

$\GL_2(\Z/272\Z)$-generators: $\begin{bmatrix}17&124\\228&219\end{bmatrix}$, $\begin{bmatrix}31&192\\224&89\end{bmatrix}$, $\begin{bmatrix}159&236\\108&197\end{bmatrix}$, $\begin{bmatrix}175&64\\60&261\end{bmatrix}$, $\begin{bmatrix}185&176\\88&221\end{bmatrix}$, $\begin{bmatrix}257&40\\72&163\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 272.192.2-272.k.1.1, 272.192.2-272.k.1.2, 272.192.2-272.k.1.3, 272.192.2-272.k.1.4, 272.192.2-272.k.1.5, 272.192.2-272.k.1.6, 272.192.2-272.k.1.7, 272.192.2-272.k.1.8, 272.192.2-272.k.1.9, 272.192.2-272.k.1.10, 272.192.2-272.k.1.11, 272.192.2-272.k.1.12, 272.192.2-272.k.1.13, 272.192.2-272.k.1.14, 272.192.2-272.k.1.15, 272.192.2-272.k.1.16, 272.192.2-272.k.1.17, 272.192.2-272.k.1.18, 272.192.2-272.k.1.19, 272.192.2-272.k.1.20, 272.192.2-272.k.1.21, 272.192.2-272.k.1.22, 272.192.2-272.k.1.23, 272.192.2-272.k.1.24, 272.192.2-272.k.1.25, 272.192.2-272.k.1.26, 272.192.2-272.k.1.27, 272.192.2-272.k.1.28, 272.192.2-272.k.1.29, 272.192.2-272.k.1.30, 272.192.2-272.k.1.31, 272.192.2-272.k.1.32
Cyclic 272-isogeny field degree: $72$
Cyclic 272-torsion field degree: $4608$
Full 272-torsion field degree: $20054016$

Rational points

This modular curve has 2 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
8.48.0.c.1 $8$ $2$ $2$ $0$ $0$

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

Covering curve Level Index Degree Genus
272.192.5.bf.1 $272$ $2$ $2$ $5$
272.192.5.bf.2 $272$ $2$ $2$ $5$
272.192.5.bj.1 $272$ $2$ $2$ $5$
272.192.5.bj.2 $272$ $2$ $2$ $5$
272.192.5.cx.1 $272$ $2$ $2$ $5$
272.192.5.cx.2 $272$ $2$ $2$ $5$
272.192.5.cz.1 $272$ $2$ $2$ $5$
272.192.5.cz.2 $272$ $2$ $2$ $5$
272.192.5.fm.1 $272$ $2$ $2$ $5$
272.192.5.fm.2 $272$ $2$ $2$ $5$
272.192.5.fn.1 $272$ $2$ $2$ $5$
272.192.5.fn.2 $272$ $2$ $2$ $5$
272.192.5.fr.1 $272$ $2$ $2$ $5$
272.192.5.fr.2 $272$ $2$ $2$ $5$
272.192.5.fv.1 $272$ $2$ $2$ $5$
272.192.5.fv.2 $272$ $2$ $2$ $5$
272.192.7.bc.1 $272$ $2$ $2$ $7$
272.192.7.be.1 $272$ $2$ $2$ $7$
272.192.7.bw.1 $272$ $2$ $2$ $7$
272.192.7.bx.1 $272$ $2$ $2$ $7$
272.192.7.di.1 $272$ $2$ $2$ $7$
272.192.7.dk.1 $272$ $2$ $2$ $7$
272.192.7.do.1 $272$ $2$ $2$ $7$
272.192.7.dq.1 $272$ $2$ $2$ $7$