# Properties

 Label 8550.be Number of curves $2$ Conductor $8550$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("be1")

sage: E.isogeny_class()

## Elliptic curves in class 8550.be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.be1 8550bm2 $$[1, -1, 1, -15305, 1186697]$$ $$-1392225385/1316928$$ $$-375015825000000$$ $$$$ $$34560$$ $$1.4928$$
8550.be2 8550bm1 $$[1, -1, 1, 1570, -28303]$$ $$1503815/2052$$ $$-584339062500$$ $$[]$$ $$11520$$ $$0.94354$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8550.be have rank $$1$$.

## Complex multiplication

The elliptic curves in class 8550.be do not have complex multiplication.

## Modular form8550.2.a.be

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 2q^{7} + q^{8} - 3q^{11} + 2q^{13} + 2q^{14} + q^{16} - 6q^{17} + q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 