# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 8550.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.i1 8550a2 $$[1, -1, 0, -7467, 249191]$$ $$149721291/722$$ $$222048843750$$ $$$$ $$12288$$ $$1.0258$$
8550.i2 8550a1 $$[1, -1, 0, -717, -559]$$ $$132651/76$$ $$23373562500$$ $$$$ $$6144$$ $$0.67927$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8550.2.a.i

sage: E.q_eigenform(10)

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