# Properties

 Label 28560.cj Number of curves $2$ Conductor $28560$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cj1")

sage: E.isogeny_class()

## Elliptic curves in class 28560.cj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28560.cj1 28560dh2 $$[0, 1, 0, -8296, -217036]$$ $$15417797707369/4080067320$$ $$16711955742720$$ $$$$ $$55296$$ $$1.2458$$
28560.cj2 28560dh1 $$[0, 1, 0, 1304, -21196]$$ $$59822347031/83966400$$ $$-343926374400$$ $$$$ $$27648$$ $$0.89927$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 28560.cj have rank $$0$$.

## Complex multiplication

The elliptic curves in class 28560.cj do not have complex multiplication.

## Modular form 28560.2.a.cj

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - q^{7} + q^{9} - 2q^{11} - 2q^{13} - q^{15} + q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 