# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 8550.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.o1 8550j2 $$[1, -1, 0, -89442, -10259784]$$ $$6947097508441/10687500$$ $$121737304687500$$ $$$$ $$36864$$ $$1.6021$$
8550.o2 8550j1 $$[1, -1, 0, -3942, -256284]$$ $$-594823321/2166000$$ $$-24672093750000$$ $$$$ $$18432$$ $$1.2555$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8550.2.a.o

sage: E.q_eigenform(10)

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