Properties

Label 280.24.0.cv.1
Level $280$
Index $24$
Genus $0$
Cusps $6$
$\Q$-cusps $0$

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Invariants

Level: $280$ $\SL_2$-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

$\GL_2(\Z/280\Z)$-generators: $\begin{bmatrix}133&228\\66&227\end{bmatrix}$, $\begin{bmatrix}137&132\\267&15\end{bmatrix}$, $\begin{bmatrix}173&64\\142&137\end{bmatrix}$, $\begin{bmatrix}183&260\\179&17\end{bmatrix}$, $\begin{bmatrix}205&192\\263&11\end{bmatrix}$, $\begin{bmatrix}225&32\\33&257\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 280.48.0-280.cv.1.1, 280.48.0-280.cv.1.2, 280.48.0-280.cv.1.3, 280.48.0-280.cv.1.4, 280.48.0-280.cv.1.5, 280.48.0-280.cv.1.6, 280.48.0-280.cv.1.7, 280.48.0-280.cv.1.8, 280.48.0-280.cv.1.9, 280.48.0-280.cv.1.10, 280.48.0-280.cv.1.11, 280.48.0-280.cv.1.12, 280.48.0-280.cv.1.13, 280.48.0-280.cv.1.14, 280.48.0-280.cv.1.15, 280.48.0-280.cv.1.16
Cyclic 280-isogeny field degree: $96$
Cyclic 280-torsion field degree: $9216$
Full 280-torsion field degree: $61931520$

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
28.12.0.g.1 $28$ $2$ $2$ $0$ $0$
40.12.0.bb.1 $40$ $2$ $2$ $0$ $0$
280.12.0.y.1 $280$ $2$ $2$ $0$ $?$

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

Covering curve Level Index Degree Genus
280.120.8.eh.1 $280$ $5$ $5$ $8$
280.144.7.ie.1 $280$ $6$ $6$ $7$
280.192.11.jz.1 $280$ $8$ $8$ $11$
280.240.15.kr.1 $280$ $10$ $10$ $15$