# Properties

 Label 6930.bj Number of curves $2$ Conductor $6930$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bj1")

sage: E.isogeny_class()

## Elliptic curves in class 6930.bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.bj1 6930v1 $$[1, -1, 1, -20927, 1170279]$$ $$37537160298467283/5519360000$$ $$149022720000$$ $$[2]$$ $$14336$$ $$1.1582$$ $$\Gamma_0(N)$$-optimal
6930.bj2 6930v2 $$[1, -1, 1, -19007, 1392231]$$ $$-28124139978713043/14526050000000$$ $$-392203350000000$$ $$[2]$$ $$28672$$ $$1.5048$$

## Rank

sage: E.rank()

The elliptic curves in class 6930.bj have rank $$1$$.

## Complex multiplication

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

## Modular form6930.2.a.bj

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.