# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 189618b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.bj1 189618b1 $$[1, 0, 0, -15805, -546079]$$ $$90458382169/25788048$$ $$124473982178832$$ $$$$ $$1075200$$ $$1.4112$$ $$\Gamma_0(N)$$-optimal
189618.bj2 189618b2 $$[1, 0, 0, 41655, -3591459]$$ $$1656015369191/2114999172$$ $$-10208697038402148$$ $$$$ $$2150400$$ $$1.7578$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 189618.2.a.b

sage: E.q_eigenform(10)

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