Properties

Label 272.48.0-272.m.1.18
Level $272$
Index $48$
Genus $0$
Cusps $6$
$\Q$-cusps $2$

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Invariants

Level: $272$ $\SL_2$-level: $16$
Index: $48$ $\PSL_2$-index:$24$
Genus: $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps: $6$ (of which $2$ are rational) Cusp widths $1^{2}\cdot2^{3}\cdot16$ Cusp orbits $1^{2}\cdot2^{2}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
$\Q$-gonality: $1$
$\overline{\Q}$-gonality: $1$
Rational cusps: $2$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 16D0

Level structure

$\GL_2(\Z/272\Z)$-generators: $\begin{bmatrix}57&186\\62&253\end{bmatrix}$, $\begin{bmatrix}129&156\\28&225\end{bmatrix}$, $\begin{bmatrix}168&115\\173&150\end{bmatrix}$, $\begin{bmatrix}193&46\\152&231\end{bmatrix}$, $\begin{bmatrix}220&85\\265&208\end{bmatrix}$
Contains $-I$: no $\quad$ (see 272.24.0.m.1 for the level structure with $-I$)
Cyclic 272-isogeny field degree: $36$
Cyclic 272-torsion field degree: $2304$
Full 272-torsion field degree: $40108032$

Models

This modular curve is isomorphic to $\mathbb{P}^1$.

Rational points

This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
16.24.0-8.n.1.8 $16$ $2$ $2$ $0$ $0$
136.24.0-8.n.1.4 $136$ $2$ $2$ $0$ $?$

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

Covering curve Level Index Degree Genus
272.96.0-272.f.2.23 $272$ $2$ $2$ $0$
272.96.0-272.g.1.11 $272$ $2$ $2$ $0$
272.96.0-272.l.1.13 $272$ $2$ $2$ $0$
272.96.0-272.n.1.11 $272$ $2$ $2$ $0$
272.96.0-272.bb.2.1 $272$ $2$ $2$ $0$
272.96.0-272.bc.2.5 $272$ $2$ $2$ $0$
272.96.0-272.be.2.5 $272$ $2$ $2$ $0$
272.96.0-272.bh.2.3 $272$ $2$ $2$ $0$
272.96.0-272.bm.1.14 $272$ $2$ $2$ $0$
272.96.0-272.bn.1.10 $272$ $2$ $2$ $0$
272.96.0-272.bu.1.10 $272$ $2$ $2$ $0$
272.96.0-272.bv.1.12 $272$ $2$ $2$ $0$
272.96.0-272.ca.1.6 $272$ $2$ $2$ $0$
272.96.0-272.cb.1.14 $272$ $2$ $2$ $0$
272.96.0-272.ce.1.14 $272$ $2$ $2$ $0$
272.96.0-272.cf.1.10 $272$ $2$ $2$ $0$
272.96.1-272.bg.1.10 $272$ $2$ $2$ $1$
272.96.1-272.bh.2.12 $272$ $2$ $2$ $1$
272.96.1-272.bk.1.8 $272$ $2$ $2$ $1$
272.96.1-272.bl.1.10 $272$ $2$ $2$ $1$
272.96.1-272.bs.1.12 $272$ $2$ $2$ $1$
272.96.1-272.bt.1.10 $272$ $2$ $2$ $1$
272.96.1-272.ca.1.10 $272$ $2$ $2$ $1$
272.96.1-272.cb.2.12 $272$ $2$ $2$ $1$