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Properties

Label 176.96.2.a.1
Level $176$
Index $96$
Genus $2$
Cusps $14$
$\Q$-cusps $2$

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Invariants

Level: $176$ $\SL_2$-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

$\GL_2(\Z/176\Z)$-generators: $\begin{bmatrix}9&172\\88&3\end{bmatrix}$, $\begin{bmatrix}23&80\\28&173\end{bmatrix}$, $\begin{bmatrix}73&72\\68&149\end{bmatrix}$, $\begin{bmatrix}97&152\\92&99\end{bmatrix}$, $\begin{bmatrix}137&28\\172&115\end{bmatrix}$, $\begin{bmatrix}151&92\\116&7\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 176.192.2-176.a.1.1, 176.192.2-176.a.1.2, 176.192.2-176.a.1.3, 176.192.2-176.a.1.4, 176.192.2-176.a.1.5, 176.192.2-176.a.1.6, 176.192.2-176.a.1.7, 176.192.2-176.a.1.8, 176.192.2-176.a.1.9, 176.192.2-176.a.1.10, 176.192.2-176.a.1.11, 176.192.2-176.a.1.12, 176.192.2-176.a.1.13, 176.192.2-176.a.1.14, 176.192.2-176.a.1.15, 176.192.2-176.a.1.16, 176.192.2-176.a.1.17, 176.192.2-176.a.1.18, 176.192.2-176.a.1.19, 176.192.2-176.a.1.20, 176.192.2-176.a.1.21, 176.192.2-176.a.1.22, 176.192.2-176.a.1.23, 176.192.2-176.a.1.24, 176.192.2-176.a.1.25, 176.192.2-176.a.1.26, 176.192.2-176.a.1.27, 176.192.2-176.a.1.28, 176.192.2-176.a.1.29, 176.192.2-176.a.1.30, 176.192.2-176.a.1.31, 176.192.2-176.a.1.32
Cyclic 176-isogeny field degree: $48$
Cyclic 176-torsion field degree: $1920$
Full 176-torsion field degree: $3379200$

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
176.192.5.a.1 $176$ $2$ $2$ $5$
176.192.5.a.2 $176$ $2$ $2$ $5$
176.192.5.e.1 $176$ $2$ $2$ $5$
176.192.5.e.2 $176$ $2$ $2$ $5$
176.192.5.i.1 $176$ $2$ $2$ $5$
176.192.5.i.2 $176$ $2$ $2$ $5$
176.192.5.j.1 $176$ $2$ $2$ $5$
176.192.5.j.2 $176$ $2$ $2$ $5$
176.192.5.bl.1 $176$ $2$ $2$ $5$
176.192.5.bl.2 $176$ $2$ $2$ $5$
176.192.5.bo.1 $176$ $2$ $2$ $5$
176.192.5.bo.4 $176$ $2$ $2$ $5$
176.192.5.co.1 $176$ $2$ $2$ $5$
176.192.5.co.2 $176$ $2$ $2$ $5$
176.192.5.cs.1 $176$ $2$ $2$ $5$
176.192.5.cs.2 $176$ $2$ $2$ $5$
176.192.7.a.1 $176$ $2$ $2$ $7$
176.192.7.c.1 $176$ $2$ $2$ $7$
176.192.7.e.1 $176$ $2$ $2$ $7$
176.192.7.g.1 $176$ $2$ $2$ $7$
176.192.7.o.1 $176$ $2$ $2$ $7$
176.192.7.q.1 $176$ $2$ $2$ $7$
176.192.7.w.1 $176$ $2$ $2$ $7$
176.192.7.y.1 $176$ $2$ $2$ $7$