# Properties

 Label 6930p Number of curves 4 Conductor 6930 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6930.o1")

sage: E.isogeny_class()

## Elliptic curves in class 6930p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6930.o3 6930p1 [1, -1, 0, -504, -84672]  13824 $$\Gamma_0(N)$$-optimal
6930.o2 6930p2 [1, -1, 0, -32184, -2194560]  27648
6930.o4 6930p3 [1, -1, 0, 4536, 2283120]  41472
6930.o1 6930p4 [1, -1, 0, -235044, 42676308]  82944

## Rank

sage: E.rank()

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

## Modular form6930.2.a.o

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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 