# Properties

 Label 3264.p Number of curves $2$ Conductor $3264$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("p1")

E.isogeny_class()

## Elliptic curves in class 3264.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3264.p1 3264t1 $$[0, -1, 0, -161, -447]$$ $$1771561/612$$ $$160432128$$ $$$$ $$1536$$ $$0.27619$$ $$\Gamma_0(N)$$-optimal
3264.p2 3264t2 $$[0, -1, 0, 479, -3647]$$ $$46268279/46818$$ $$-12273057792$$ $$$$ $$3072$$ $$0.62277$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3264.2.a.p

sage: E.q_eigenform(10)

$$q - q^{3} + 4 q^{5} + 2 q^{7} + q^{9} + 6 q^{13} - 4 q^{15} - q^{17} + 4 q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 