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Properties

Label 120.24.0.ea.1
Level $120$
Index $24$
Genus $0$
Cusps $6$
$\Q$-cusps $0$

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Invariants

Level: $120$ $\SL_2$-level: $8$
Index: $24$ $\PSL_2$-index:$24$
Genus: $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps: $6$ (none of which are rational) Cusp widths $2^{4}\cdot8^{2}$ Cusp orbits $2^{3}$
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: 8G0

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}7&60\\106&119\end{bmatrix}$, $\begin{bmatrix}9&92\\25&97\end{bmatrix}$, $\begin{bmatrix}23&32\\12&77\end{bmatrix}$, $\begin{bmatrix}45&92\\43&59\end{bmatrix}$, $\begin{bmatrix}91&40\\3&11\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 120.48.0-120.ea.1.1, 120.48.0-120.ea.1.2, 120.48.0-120.ea.1.3, 120.48.0-120.ea.1.4, 120.48.0-120.ea.1.5, 120.48.0-120.ea.1.6, 120.48.0-120.ea.1.7, 120.48.0-120.ea.1.8, 120.48.0-120.ea.1.9, 120.48.0-120.ea.1.10, 120.48.0-120.ea.1.11, 120.48.0-120.ea.1.12, 120.48.0-120.ea.1.13, 120.48.0-120.ea.1.14, 120.48.0-120.ea.1.15, 120.48.0-120.ea.1.16
Cyclic 120-isogeny field degree: $48$
Cyclic 120-torsion field degree: $1536$
Full 120-torsion field degree: $1474560$

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
24.12.0.ba.1 $24$ $2$ $2$ $0$ $0$
40.12.0.ba.1 $40$ $2$ $2$ $0$ $0$
60.12.0.h.1 $60$ $2$ $2$ $0$ $0$

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

Covering curve Level Index Degree Genus
120.72.4.oe.1 $120$ $3$ $3$ $4$
120.96.3.qg.1 $120$ $4$ $4$ $3$
120.120.8.fy.1 $120$ $5$ $5$ $8$
120.144.7.dxb.1 $120$ $6$ $6$ $7$
120.240.15.nw.1 $120$ $10$ $10$ $15$