# Properties

 Label 6930.g Number of curves 2 Conductor 6930 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6930.g1")

sage: E.isogeny_class()

## Elliptic curves in class 6930.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6930.g1 6930j1 [1, -1, 0, -44955, 3679825]  23040 $$\Gamma_0(N)$$-optimal
6930.g2 6930j2 [1, -1, 0, -42525, 4093411]  46080

## Rank

sage: E.rank()

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

## Modular form6930.2.a.g

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 