# Properties

 Label 6930.b Number of curves 4 Conductor 6930 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6930.b1")

sage: E.isogeny_class()

## Elliptic curves in class 6930.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6930.b1 6930f3 [1, -1, 0, -443520, 113799816] [2] 24576
6930.b2 6930f2 [1, -1, 0, -27720, 1783296] [2, 2] 12288
6930.b3 6930f4 [1, -1, 0, -26640, 1927800] [2] 24576
6930.b4 6930f1 [1, -1, 0, -1800, 25920] [2] 6144 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form6930.2.a.b

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.