# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bm1")

sage: E.isogeny_class()

## Elliptic curves in class 6930.bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6930.bm1 6930bk4 $$[1, -1, 1, -140837, -15663139]$$ $$423783056881319689/99207416000000$$ $$72322206264000000$$ $$$$ $$82944$$ $$1.9468$$
6930.bm2 6930bk2 $$[1, -1, 1, -131702, -18363571]$$ $$346553430870203929/8300600$$ $$6051137400$$ $$$$ $$27648$$ $$1.3975$$
6930.bm3 6930bk1 $$[1, -1, 1, -8222, -286099]$$ $$-84309998289049/414124480$$ $$-301896745920$$ $$$$ $$13824$$ $$1.0509$$ $$\Gamma_0(N)$$-optimal
6930.bm4 6930bk3 $$[1, -1, 1, 20443, -1535011]$$ $$1296134247276791/2137096192000$$ $$-1557943123968000$$ $$$$ $$41472$$ $$1.6003$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form6930.2.a.bm

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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 