# Properties

 Label 20160.fg Number of curves $6$ Conductor $20160$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("20160.fg1")

sage: E.isogeny_class()

## Elliptic curves in class 20160.fg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.fg1 20160fg5 [0, 0, 0, -377292, -89197936] [2] 131072
20160.fg2 20160fg3 [0, 0, 0, -24492, -1280176] [2, 2] 65536
20160.fg3 20160fg2 [0, 0, 0, -6492, 181424] [2, 2] 32768
20160.fg4 20160fg1 [0, 0, 0, -6312, 193016] [2] 16384 $$\Gamma_0(N)$$-optimal
20160.fg5 20160fg4 [0, 0, 0, 8628, 901136] [2] 65536
20160.fg6 20160fg6 [0, 0, 0, 40308, -6904816] [2] 131072

## Rank

sage: E.rank()

The elliptic curves in class 20160.fg have rank $$1$$.

## Modular form 20160.2.a.fg

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} + 4q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.