# Properties

 Label 6930.f Number of curves 4 Conductor 6930 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6930.f1")
sage: E.isogeny_class()

## Elliptic curves in class 6930.f

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
6930.f1 6930h4 [1, -1, 0, -31680, 2166426] 6 27648
6930.f2 6930h2 [1, -1, 0, -2430, -43524] 2 9216
6930.f3 6930h3 [1, -1, 0, -810, 73440] 6 13824
6930.f4 6930h1 [1, -1, 0, 90, -2700] 2 4608 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6930.f have rank $$0$$.

## Modular form6930.2.a.f

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 