# Properties

 Label 6930.bk Number of curves $2$ Conductor $6930$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 6930.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.bk1 6930bj2 $$[1, -1, 1, -662, 6711]$$ $$43949604889/42350$$ $$30873150$$ $$$$ $$3072$$ $$0.35829$$
6930.bk2 6930bj1 $$[1, -1, 1, -32, 159]$$ $$-4826809/10780$$ $$-7858620$$ $$$$ $$1536$$ $$0.011719$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6930.bk have rank $$0$$.

## Complex multiplication

The elliptic curves in class 6930.bk do not have complex multiplication.

## Modular form6930.2.a.bk

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} + q^{11} + 2q^{13} + q^{14} + q^{16} - 2q^{17} + 6q^{19} + O(q^{20})$$ ## 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. 