# Properties

 Label 221067.ba Number of curves $2$ Conductor $221067$ CM no Rank $0$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("ba1")

sage: E.isogeny_class()

## Elliptic curves in class 221067.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
221067.ba1 221067ba2 $$[1, -1, 0, -2182923, 1157722330]$$ $$669233048723/50759541$$ $$87252801680436806799$$ $$$$ $$4866048$$ $$2.5713$$
221067.ba2 221067ba1 $$[1, -1, 0, -445968, -93232661]$$ $$5706550403/1112643$$ $$1912570860720081177$$ $$$$ $$2433024$$ $$2.2247$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 221067.ba have rank $$0$$.

## Complex multiplication

The elliptic curves in class 221067.ba do not have complex multiplication.

## Modular form 221067.2.a.ba

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - 2q^{5} + q^{7} - 3q^{8} - 2q^{10} + q^{14} - q^{16} + 2q^{17} - 2q^{19} + O(q^{20})$$ ## 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 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. 