# Properties

 Label 8550.g Number of curves $2$ Conductor $8550$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 8550.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.g1 8550f2 $$[1, -1, 0, -364167, -84494259]$$ $$468898230633769/5540400$$ $$63108618750000$$ $$$$ $$73728$$ $$1.7980$$
8550.g2 8550f1 $$[1, -1, 0, -22167, -1388259]$$ $$-105756712489/12476160$$ $$-142111260000000$$ $$$$ $$36864$$ $$1.4514$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8550.g have rank $$0$$.

## Complex multiplication

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

## Modular form8550.2.a.g

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 