# Properties

 Label 6930.k Number of curves 2 Conductor 6930 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6930.k1")

sage: E.isogeny_class()

## Elliptic curves in class 6930.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6930.k1 6930d1 [1, -1, 0, -2364, 44828]  6144 $$\Gamma_0(N)$$-optimal
6930.k2 6930d2 [1, -1, 0, -2094, 55250]  12288

## Rank

sage: E.rank()

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

## Modular form6930.2.a.k

sage: E.q_eigenform(10)

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

## 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. 