# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("6930.n1")

sage: E.isogeny_class()

## Elliptic curves in class 6930e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6930.n3 6930e1 [1, -1, 0, -264, 7920]  6912 $$\Gamma_0(N)$$-optimal
6930.n2 6930e2 [1, -1, 0, -7764, 264420]  13824
6930.n4 6930e3 [1, -1, 0, 2361, -204355]  20736
6930.n1 6930e4 [1, -1, 0, -40839, -2960515]  41472

## Rank

sage: E.rank()

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

## Modular form6930.2.a.n

sage: E.q_eigenform(10)

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

## 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. 