# Properties

 Label 189618bj Number of curves $2$ Conductor $189618$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bj1")

sage: E.isogeny_class()

## Elliptic curves in class 189618bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.b2 189618bj1 $$[1, 1, 0, -69592006, -214810557164]$$ $$7722211175253055152433/340131399900069888$$ $$1641749302220256436027392$$ $$$$ $$35043840$$ $$3.4096$$ $$\Gamma_0(N)$$-optimal
189618.b1 189618bj2 $$[1, 1, 0, -187270086, 703054931220]$$ $$150476552140919246594353/42832838728685592576$$ $$206745931471168176416169984$$ $$$$ $$70087680$$ $$3.7561$$

## Rank

sage: E.rank()

The elliptic curves in class 189618bj have rank $$0$$.

## Complex multiplication

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

## Modular form 189618.2.a.bj

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - 2q^{5} + q^{6} + 2q^{7} - q^{8} + q^{9} + 2q^{10} - q^{11} - q^{12} - 2q^{14} + 2q^{15} + q^{16} + q^{17} - q^{18} + 2q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 