# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3264.bc1")

sage: E.isogeny_class()

## Elliptic curves in class 3264bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3264.bc5 3264bc1 [0, 1, 0, -2177, -36993] [2] 3072 $$\Gamma_0(N)$$-optimal
3264.bc4 3264bc2 [0, 1, 0, -7297, 195455] [2, 2] 6144
3264.bc2 3264bc3 [0, 1, 0, -110977, 14192255] [2, 2] 12288
3264.bc6 3264bc4 [0, 1, 0, 14463, 1157247] [2] 12288
3264.bc1 3264bc5 [0, 1, 0, -1775617, 910101503] [4] 24576
3264.bc3 3264bc6 [0, 1, 0, -105217, 15737087] [2] 24576

## Rank

sage: E.rank()

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

## Modular form3264.2.a.bc

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.