Properties

Label 160.384.5-160.cw.1.5
Level $160$
Index $384$
Genus $5$
Cusps $24$
$\Q$-cusps $0$

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Invariants

Level: $160$ $\SL_2$-level: $32$ Newform level: $1$
Index: $384$ $\PSL_2$-index:$192$
Genus: $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$
Cusps: $24$ (none of which are rational) Cusp widths $2^{8}\cdot4^{12}\cdot32^{4}$ Cusp orbits $2^{4}\cdot4^{4}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $2 \le \gamma \le 8$
$\overline{\Q}$-gonality: $2 \le \gamma \le 5$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 32N5

Level structure

$\GL_2(\Z/160\Z)$-generators: $\begin{bmatrix}9&112\\55&87\end{bmatrix}$, $\begin{bmatrix}65&48\\53&31\end{bmatrix}$, $\begin{bmatrix}65&128\\118&41\end{bmatrix}$, $\begin{bmatrix}133&72\\154&137\end{bmatrix}$
Contains $-I$: no $\quad$ (see 160.192.5.cw.1 for the level structure with $-I$)
Cyclic 160-isogeny field degree: $24$
Cyclic 160-torsion field degree: $384$
Full 160-torsion field degree: $491520$

Rational points

This modular curve has no real points and no $\Q_p$ points for $p=31$, and therefore no rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
16.192.1-16.l.1.2 $16$ $2$ $2$ $1$ $0$
160.192.1-16.l.1.2 $160$ $2$ $2$ $1$ $?$
160.192.2-160.h.1.1 $160$ $2$ $2$ $2$ $?$
160.192.2-160.h.1.22 $160$ $2$ $2$ $2$ $?$
160.192.2-160.j.1.5 $160$ $2$ $2$ $2$ $?$
160.192.2-160.j.1.22 $160$ $2$ $2$ $2$ $?$