# Properties

 Label 4410.bk Number of curves $2$ Conductor $4410$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bk1")

sage: E.isogeny_class()

## Elliptic curves in class 4410.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4410.bk1 4410x2 $$[1, -1, 1, -791237, 271095661]$$ $$68971442301/400$$ $$317712018632400$$ $$$$ $$43008$$ $$1.9729$$
4410.bk2 4410x1 $$[1, -1, 1, -50357, 4082509]$$ $$17779581/1280$$ $$1016678459623680$$ $$$$ $$21504$$ $$1.6263$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4410.bk have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4410.bk do not have complex multiplication.

## Modular form4410.2.a.bk

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + 2q^{11} + 2q^{13} + q^{16} + 2q^{17} + 6q^{19} + O(q^{20})$$ ## 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. 