# Properties

 Label 203280dj Number of curves $4$ Conductor $203280$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dj1")

sage: E.isogeny_class()

## Elliptic curves in class 203280dj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
203280.bp3 203280dj1 $$[0, -1, 0, -322021, 71484976]$$ $$-130287139815424/2250652635$$ $$-63794694923411760$$ $$$$ $$2488320$$ $$2.0225$$ $$\Gamma_0(N)$$-optimal
203280.bp2 203280dj2 $$[0, -1, 0, -5173516, 4530979180]$$ $$33766427105425744/9823275$$ $$4455047905862400$$ $$$$ $$4976640$$ $$2.3691$$
203280.bp4 203280dj3 $$[0, -1, 0, 1246139, 341639740]$$ $$7549996227362816/6152409907875$$ $$-174389911180879086000$$ $$$$ $$7464960$$ $$2.5718$$
203280.bp1 203280dj4 $$[0, -1, 0, -6001156, 2985452956]$$ $$52702650535889104/22020583921875$$ $$9986766764344524000000$$ $$$$ $$14929920$$ $$2.9184$$

## Rank

sage: E.rank()

The elliptic curves in class 203280dj have rank $$0$$.

## Complex multiplication

The elliptic curves in class 203280dj do not have complex multiplication.

## Modular form 203280.2.a.dj

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + q^{7} + q^{9} - 2q^{13} + q^{15} + 6q^{17} + 8q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 