# Properties

 Label 6930.bc Number of curves $4$ Conductor $6930$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 6930.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.bc1 6930be3 $$[1, -1, 1, -26916647, -53548383009]$$ $$2958414657792917260183849/12401051653985258880$$ $$9040366655755253723520$$ $$[2]$$ $$802816$$ $$3.0677$$
6930.bc2 6930be2 $$[1, -1, 1, -2523047, 88264671]$$ $$2436531580079063806249/1405478914998681600$$ $$1024594129034038886400$$ $$[2, 2]$$ $$401408$$ $$2.7211$$
6930.bc3 6930be1 $$[1, -1, 1, -1785767, 916672479]$$ $$863913648706111516969/2486234429521920$$ $$1812464899121479680$$ $$[4]$$ $$200704$$ $$2.3745$$ $$\Gamma_0(N)$$-optimal
6930.bc4 6930be4 $$[1, -1, 1, 10074073, 697965279]$$ $$155099895405729262880471/90047655797243760000$$ $$-65644741076190701040000$$ $$[2]$$ $$802816$$ $$3.0677$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form6930.2.a.bc

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.