# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 6930.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.k1 6930d1 $$[1, -1, 0, -2364, 44828]$$ $$74246873427/16940$$ $$333430020$$ $$[2]$$ $$6144$$ $$0.62720$$ $$\Gamma_0(N)$$-optimal
6930.k2 6930d2 $$[1, -1, 0, -2094, 55250]$$ $$-51603494067/35870450$$ $$-706038067350$$ $$[2]$$ $$12288$$ $$0.97377$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form6930.2.a.k

sage: E.q_eigenform(10)

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

## 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.