# Properties

 Label 3264bc Number of curves $6$ Conductor $3264$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("bc1")

E.isogeny_class()

## Elliptic curves in class 3264bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3264.bc5 3264bc1 $$[0, 1, 0, -2177, -36993]$$ $$4354703137/352512$$ $$92408905728$$ $$[2]$$ $$3072$$ $$0.84708$$ $$\Gamma_0(N)$$-optimal
3264.bc4 3264bc2 $$[0, 1, 0, -7297, 195455]$$ $$163936758817/30338064$$ $$7952941449216$$ $$[2, 2]$$ $$6144$$ $$1.1937$$
3264.bc2 3264bc3 $$[0, 1, 0, -110977, 14192255]$$ $$576615941610337/27060804$$ $$7093827403776$$ $$[2, 2]$$ $$12288$$ $$1.5402$$
3264.bc6 3264bc4 $$[0, 1, 0, 14463, 1157247]$$ $$1276229915423/2927177028$$ $$-767341894828032$$ $$[2]$$ $$12288$$ $$1.5402$$
3264.bc1 3264bc5 $$[0, 1, 0, -1775617, 910101503]$$ $$2361739090258884097/5202$$ $$1363673088$$ $$[4]$$ $$24576$$ $$1.8868$$
3264.bc3 3264bc6 $$[0, 1, 0, -105217, 15737087]$$ $$-491411892194497/125563633938$$ $$-32915753255043072$$ $$[2]$$ $$24576$$ $$1.8868$$

## Rank

sage: E.rank()

The elliptic curves in class 3264bc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3264bc do not have complex multiplication.

## Modular form3264.2.a.bc

sage: E.q_eigenform(10)

$$q + q^{3} + 2 q^{5} + q^{9} - 4 q^{11} + 2 q^{13} + 2 q^{15} + q^{17} + 4 q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.