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Properties

Label 280.12.0.a.1
Level $280$
Index $12$
Genus $0$
Cusps $4$
$\Q$-cusps $2$

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Invariants

Level: $280$ $\SL_2$-level: $4$
Index: $12$ $\PSL_2$-index:$12$
Genus: $0 = 1 + \frac{ 12 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$
Cusps: $4$ (of which $2$ are rational) Cusp widths $2^{2}\cdot4^{2}$ Cusp orbits $1^{2}\cdot2$
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: 4E0

Level structure

$\GL_2(\Z/280\Z)$-generators: $\begin{bmatrix}121&130\\90&79\end{bmatrix}$, $\begin{bmatrix}161&64\\108&45\end{bmatrix}$, $\begin{bmatrix}213&174\\166&67\end{bmatrix}$, $\begin{bmatrix}257&140\\36&79\end{bmatrix}$, $\begin{bmatrix}263&192\\48&223\end{bmatrix}$, $\begin{bmatrix}279&228\\214&101\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 280.24.0-280.a.1.1, 280.24.0-280.a.1.2, 280.24.0-280.a.1.3, 280.24.0-280.a.1.4, 280.24.0-280.a.1.5, 280.24.0-280.a.1.6, 280.24.0-280.a.1.7, 280.24.0-280.a.1.8, 280.24.0-280.a.1.9, 280.24.0-280.a.1.10, 280.24.0-280.a.1.11, 280.24.0-280.a.1.12, 280.24.0-280.a.1.13, 280.24.0-280.a.1.14, 280.24.0-280.a.1.15, 280.24.0-280.a.1.16
Cyclic 280-isogeny field degree: $192$
Cyclic 280-torsion field degree: $18432$
Full 280-torsion field degree: $123863040$

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
$X(2)$ $2$ $2$ $2$ $0$ $0$
280.6.0.c.1 $280$ $2$ $2$ $0$ $?$
280.6.0.f.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
280.24.0.a.1 $280$ $2$ $2$ $0$
280.24.0.b.1 $280$ $2$ $2$ $0$
280.24.0.e.1 $280$ $2$ $2$ $0$
280.24.0.g.1 $280$ $2$ $2$ $0$
280.24.0.h.1 $280$ $2$ $2$ $0$
280.24.0.i.1 $280$ $2$ $2$ $0$
280.24.0.q.1 $280$ $2$ $2$ $0$
280.24.0.r.1 $280$ $2$ $2$ $0$
280.60.4.c.1 $280$ $5$ $5$ $4$
280.72.3.c.1 $280$ $6$ $6$ $3$
280.96.5.c.1 $280$ $8$ $8$ $5$
280.120.7.c.1 $280$ $10$ $10$ $7$
280.252.16.c.1 $280$ $21$ $21$ $16$
280.336.21.c.1 $280$ $28$ $28$ $21$