# Properties

 Label 6930g Number of curves 6 Conductor 6930 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6930.a1")

sage: E.isogeny_class()

## Elliptic curves in class 6930g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6930.a5 6930g1 [1, -1, 0, 315, -25259]  8192 $$\Gamma_0(N)$$-optimal
6930.a4 6930g2 [1, -1, 0, -11205, -437675] [2, 2] 16384
6930.a2 6930g3 [1, -1, 0, -177525, -28745339]  32768
6930.a3 6930g4 [1, -1, 0, -29205, 1337125] [2, 2] 32768
6930.a1 6930g5 [1, -1, 0, -426105, 107150665]  65536
6930.a6 6930g6 [1, -1, 0, 79695, 8894785]  65536

## Rank

sage: E.rank()

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

## Modular form6930.2.a.a

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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 