# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("6930.m1")
sage: E.isogeny_class()

## Elliptic curves in class 6930m

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
6930.m3 6930m1 [1, -1, 0, -4509, 102325] 2 12288 $$\Gamma_0(N)$$-optimal
6930.m2 6930m2 [1, -1, 0, -19089, -909527] 4 24576
6930.m1 6930m3 [1, -1, 0, -296919, -62198825] 2 49152
6930.m4 6930m4 [1, -1, 0, 25461, -4553717] 2 49152

## Rank

sage: E.rank()

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

## Modular form6930.2.a.m

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 Cremona 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 Cremona labels. 