# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bb1")

sage: E.isogeny_class()

## Elliptic curves in class 8550.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8550.bb1 8550bj2 $$[1, -1, 1, -575555, -167921053]$$ $$14809006736693/34656$$ $$49344187500000$$ $$$$ $$76800$$ $$1.8700$$
8550.bb2 8550bj1 $$[1, -1, 1, -35555, -2681053]$$ $$-3491055413/175104$$ $$-249318000000000$$ $$$$ $$38400$$ $$1.5234$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8550.2.a.bb

sage: E.q_eigenform(10)

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