# Properties

 Label 20160fj Number of curves $4$ Conductor $20160$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fj1")

sage: E.isogeny_class()

## Elliptic curves in class 20160fj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20160.eg3 20160fj1 $$[0, 0, 0, -327, -1136]$$ $$82881856/36015$$ $$1680315840$$ $$[2]$$ $$12288$$ $$0.46632$$ $$\Gamma_0(N)$$-optimal
20160.eg2 20160fj2 $$[0, 0, 0, -2532, 48256]$$ $$601211584/11025$$ $$32920473600$$ $$[2, 2]$$ $$24576$$ $$0.81289$$
20160.eg1 20160fj3 $$[0, 0, 0, -40332, 3117616]$$ $$303735479048/105$$ $$2508226560$$ $$[2]$$ $$49152$$ $$1.1595$$
20160.eg4 20160fj4 $$[0, 0, 0, -12, 139984]$$ $$-8/354375$$ $$-8465264640000$$ $$[2]$$ $$49152$$ $$1.1595$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 20160fj do not have complex multiplication.

## Modular form 20160.2.a.fj

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} - 4q^{11} - 6q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.