# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 8550u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.bg2 8550u1 $$[1, -1, 1, 2020, 23647]$$ $$2161700757/1848320$$ $$-779760000000$$ $$$$ $$15360$$ $$0.96945$$ $$\Gamma_0(N)$$-optimal
8550.bg1 8550u2 $$[1, -1, 1, -9980, 215647]$$ $$260549802603/104256800$$ $$43983337500000$$ $$$$ $$30720$$ $$1.3160$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8550.2.a.u

sage: E.q_eigenform(10)

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

## 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 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. 