# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("6930.j1")

sage: E.isogeny_class()

## Elliptic curves in class 6930.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6930.j1 6930l1 [1, -1, 0, -54, 0]  1536 $$\Gamma_0(N)$$-optimal
6930.j2 6930l2 [1, -1, 0, 216, -162]  3072

## Rank

sage: E.rank()

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

## Modular form6930.2.a.j

sage: E.q_eigenform(10)

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

## 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. 