# Properties

 Label 139650.cw Number of curves $2$ Conductor $139650$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cw1")

sage: E.isogeny_class()

## Elliptic curves in class 139650.cw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.cw1 139650fm2 $$[1, 0, 1, -45726826, -124572092452]$$ $$-46017030564782549/2542728609792$$ $$-584276324635584000000000$$ $$[]$$ $$28800000$$ $$3.3182$$
139650.cw2 139650fm1 $$[1, 0, 1, 241299, 468190048]$$ $$6761990971/415984632$$ $$-95586281191734375000$$ $$[]$$ $$5760000$$ $$2.5135$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 139650.cw have rank $$1$$.

## Complex multiplication

The elliptic curves in class 139650.cw do not have complex multiplication.

## Modular form 139650.2.a.cw

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} - 3 q^{11} + q^{12} - q^{13} + q^{16} - 2 q^{17} - q^{18} + q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 