# Properties

 Label 189618bt Number of curves $2$ Conductor $189618$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bt1")

sage: E.isogeny_class()

## Elliptic curves in class 189618bt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.j1 189618bt1 $$[1, 1, 0, -1524, -11760]$$ $$81182737/35904$$ $$173301750336$$ $$$$ $$207360$$ $$0.85223$$ $$\Gamma_0(N)$$-optimal
189618.j2 189618bt2 $$[1, 1, 0, 5236, -80712]$$ $$3288008303/2517768$$ $$-12152785242312$$ $$$$ $$414720$$ $$1.1988$$

## Rank

sage: E.rank()

The elliptic curves in class 189618bt have rank $$1$$.

## Complex multiplication

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

## Modular form 189618.2.a.bt

sage: E.q_eigenform(10)

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