# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bl1")

sage: E.isogeny_class()

## Elliptic curves in class 8550.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.bl1 8550t2 $$[1, -1, 1, -121880, -16189253]$$ $$651038076963/7220000$$ $$2220488437500000$$ $$$$ $$92160$$ $$1.7590$$
8550.bl2 8550t1 $$[1, -1, 1, -13880, 226747]$$ $$961504803/486400$$ $$149590800000000$$ $$$$ $$46080$$ $$1.4125$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8550.2.a.bl

sage: E.q_eigenform(10)

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