# Properties

 Label 6930.w Number of curves $4$ Conductor $6930$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

## Elliptic curves in class 6930.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.w1 6930x3 $$[1, -1, 1, -2395013, -1426026283]$$ $$2084105208962185000201/31185000$$ $$22733865000$$ $$[2]$$ $$98304$$ $$1.9908$$
6930.w2 6930x4 $$[1, -1, 1, -162293, -18275659]$$ $$648474704552553481/176469171805080$$ $$128646026245903320$$ $$[2]$$ $$98304$$ $$1.9908$$
6930.w3 6930x2 $$[1, -1, 1, -149693, -22252219]$$ $$508859562767519881/62240270400$$ $$45373157121600$$ $$[2, 2]$$ $$49152$$ $$1.6443$$
6930.w4 6930x1 $$[1, -1, 1, -8573, -406843]$$ $$-95575628340361/43812679680$$ $$-31939443486720$$ $$[2]$$ $$24576$$ $$1.2977$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 6930.w do not have complex multiplication.

## Modular form6930.2.a.w

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.