# Properties

 Label 4032.bk Number of curves $4$ Conductor $4032$ CM no Rank $0$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 4032.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4032.bk1 4032bj4 $$[0, 0, 0, -10764, 429840]$$ $$1443468546/7$$ $$668860416$$ $$[2]$$ $$4096$$ $$0.89385$$
4032.bk2 4032bj3 $$[0, 0, 0, -2124, -29808]$$ $$11090466/2401$$ $$229419122688$$ $$[2]$$ $$4096$$ $$0.89385$$
4032.bk3 4032bj2 $$[0, 0, 0, -684, 6480]$$ $$740772/49$$ $$2341011456$$ $$[2, 2]$$ $$2048$$ $$0.54727$$
4032.bk4 4032bj1 $$[0, 0, 0, 36, 432]$$ $$432/7$$ $$-83607552$$ $$[2]$$ $$1024$$ $$0.20070$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4032.bk have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4032.bk do not have complex multiplication.

## Modular form4032.2.a.bk

sage: E.q_eigenform(10)

$$q + 2 q^{5} + q^{7} + 4 q^{11} - 2 q^{13} + 6 q^{17} + 8 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.