# Properties

 Label 189618.bb Number of curves $2$ Conductor $189618$ CM no Rank $2$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 189618.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.bb1 189618p1 $$[1, 1, 1, -510468, -127896891]$$ $$3047678972871625/304559880768$$ $$1470052373529909312$$ $$$$ $$3612672$$ $$2.2224$$ $$\Gamma_0(N)$$-optimal
189618.bb2 189618p2 $$[1, 1, 1, 631972, -617775163]$$ $$5783051584712375/37533175779528$$ $$-181165470651207766152$$ $$$$ $$7225344$$ $$2.5689$$

## Rank

sage: E.rank()

The elliptic curves in class 189618.bb have rank $$2$$.

## Complex multiplication

The elliptic curves in class 189618.bb do not have complex multiplication.

## Modular form 189618.2.a.bb

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} - 2 q^{7} + q^{8} + q^{9} - q^{11} - q^{12} - 2 q^{14} + q^{16} - q^{17} + q^{18} - 4 q^{19} + O(q^{20})$$ ## 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. 