# Properties

 Label 480240do Number of curves 2 Conductor 480240 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("480240.do1")
sage: E.isogeny_class()

## Elliptic curves in class 480240do

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
480240.do1 480240do1 [0, 0, 0, -53787, 4801034] 2 884736 $$\Gamma_0(N)$$-optimal
480240.do2 480240do2 [0, 0, 0, -50187, 5471354] 2 1769472

## Rank

sage: E.rank()

The elliptic curves in class 480240do have rank $$0$$.

## Modular form 480240.2.a.do

sage: E.q_eigenform(10)
$$q + q^{5} + 2q^{11} + 2q^{13} + 4q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 