Properties

Label 232.48.0.j.2
Level $232$
Index $48$
Genus $0$
Cusps $10$
$\Q$-cusps $0$

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Invariants

Level: $232$ $\SL_2$-level: $8$
Index: $48$ $\PSL_2$-index:$48$
Genus: $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$
Cusps: $10$ (none of which are rational) Cusp widths $4^{8}\cdot8^{2}$ Cusp orbits $2^{3}\cdot4$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
$\Q$-gonality: $1 \le \gamma \le 2$
$\overline{\Q}$-gonality: $1$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 8N0

Level structure

$\GL_2(\Z/232\Z)$-generators: $\begin{bmatrix}85&172\\208&89\end{bmatrix}$, $\begin{bmatrix}131&184\\152&29\end{bmatrix}$, $\begin{bmatrix}165&152\\60&121\end{bmatrix}$, $\begin{bmatrix}215&4\\210&231\end{bmatrix}$, $\begin{bmatrix}221&228\\34&161\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 232.96.0-232.j.2.1, 232.96.0-232.j.2.2, 232.96.0-232.j.2.3, 232.96.0-232.j.2.4, 232.96.0-232.j.2.5, 232.96.0-232.j.2.6, 232.96.0-232.j.2.7, 232.96.0-232.j.2.8, 232.96.0-232.j.2.9, 232.96.0-232.j.2.10, 232.96.0-232.j.2.11, 232.96.0-232.j.2.12, 232.96.0-232.j.2.13, 232.96.0-232.j.2.14, 232.96.0-232.j.2.15, 232.96.0-232.j.2.16
Cyclic 232-isogeny field degree: $60$
Cyclic 232-torsion field degree: $6720$
Full 232-torsion field degree: $21826560$

Models

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

Rational points

This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
8.24.0.d.1 $8$ $2$ $2$ $0$ $0$
116.24.0.c.1 $116$ $2$ $2$ $0$ $?$
232.24.0.i.1 $232$ $2$ $2$ $0$ $?$

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

Covering curve Level Index Degree Genus
232.96.1.c.1 $232$ $2$ $2$ $1$
232.96.1.t.1 $232$ $2$ $2$ $1$
232.96.1.ba.1 $232$ $2$ $2$ $1$
232.96.1.be.1 $232$ $2$ $2$ $1$
232.96.1.bs.1 $232$ $2$ $2$ $1$
232.96.1.bw.1 $232$ $2$ $2$ $1$
232.96.1.ca.1 $232$ $2$ $2$ $1$
232.96.1.cc.1 $232$ $2$ $2$ $1$