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Properties

Label 176.24.0.h.1
Level $176$
Index $24$
Genus $0$
Cusps $6$
$\Q$-cusps $2$

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Invariants

Level: $176$ $\SL_2$-level: $16$
Index: $24$ $\PSL_2$-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 $1^{4}\cdot4\cdot16$ 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: 16C0

Level structure

$\GL_2(\Z/176\Z)$-generators: $\begin{bmatrix}37&78\\136&91\end{bmatrix}$, $\begin{bmatrix}52&83\\107&76\end{bmatrix}$, $\begin{bmatrix}81&130\\6&77\end{bmatrix}$, $\begin{bmatrix}110&15\\127&110\end{bmatrix}$, $\begin{bmatrix}118&155\\57&136\end{bmatrix}$, $\begin{bmatrix}147&156\\42&173\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 176.48.0-176.h.1.1, 176.48.0-176.h.1.2, 176.48.0-176.h.1.3, 176.48.0-176.h.1.4, 176.48.0-176.h.1.5, 176.48.0-176.h.1.6, 176.48.0-176.h.1.7, 176.48.0-176.h.1.8, 176.48.0-176.h.1.9, 176.48.0-176.h.1.10, 176.48.0-176.h.1.11, 176.48.0-176.h.1.12, 176.48.0-176.h.1.13, 176.48.0-176.h.1.14, 176.48.0-176.h.1.15, 176.48.0-176.h.1.16, 176.48.0-176.h.1.17, 176.48.0-176.h.1.18, 176.48.0-176.h.1.19, 176.48.0-176.h.1.20, 176.48.0-176.h.1.21, 176.48.0-176.h.1.22, 176.48.0-176.h.1.23, 176.48.0-176.h.1.24, 176.48.0-176.h.1.25, 176.48.0-176.h.1.26, 176.48.0-176.h.1.27, 176.48.0-176.h.1.28, 176.48.0-176.h.1.29, 176.48.0-176.h.1.30, 176.48.0-176.h.1.31, 176.48.0-176.h.1.32
Cyclic 176-isogeny field degree: $24$
Cyclic 176-torsion field degree: $1920$
Full 176-torsion field degree: $13516800$

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
$X_0(8)$ $8$ $2$ $2$ $0$ $0$

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

Covering curve Level Index Degree Genus
176.48.0.bk.1 $176$ $2$ $2$ $0$
176.48.0.bk.2 $176$ $2$ $2$ $0$
176.48.0.bl.1 $176$ $2$ $2$ $0$
176.48.0.bl.2 $176$ $2$ $2$ $0$
176.48.0.bm.1 $176$ $2$ $2$ $0$
176.48.0.bm.2 $176$ $2$ $2$ $0$
176.48.0.bn.1 $176$ $2$ $2$ $0$
176.48.0.bn.2 $176$ $2$ $2$ $0$
176.48.0.bo.1 $176$ $2$ $2$ $0$
176.48.0.bo.2 $176$ $2$ $2$ $0$
176.48.0.bp.1 $176$ $2$ $2$ $0$
176.48.0.bp.2 $176$ $2$ $2$ $0$
176.48.0.bq.1 $176$ $2$ $2$ $0$
176.48.0.bq.2 $176$ $2$ $2$ $0$
176.48.0.br.1 $176$ $2$ $2$ $0$
176.48.0.br.2 $176$ $2$ $2$ $0$
176.48.1.a.2 $176$ $2$ $2$ $1$
176.48.1.f.1 $176$ $2$ $2$ $1$
176.48.1.g.1 $176$ $2$ $2$ $1$
176.48.1.j.1 $176$ $2$ $2$ $1$
176.48.1.q.1 $176$ $2$ $2$ $1$
176.48.1.t.1 $176$ $2$ $2$ $1$
176.48.1.u.1 $176$ $2$ $2$ $1$
176.48.1.x.1 $176$ $2$ $2$ $1$
176.288.19.t.1 $176$ $12$ $12$ $19$