# Properties

 Label 32064.o Number of curves 2 Conductor 32064 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("32064.o1")

sage: E.isogeny_class()

## Elliptic curves in class 32064.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
32064.o1 32064u2 [0, 1, 0, -7969, 270431]  55296
32064.o2 32064u1 [0, 1, 0, -289, 7775]  27648 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 32064.o have rank $$1$$.

## Modular form 32064.2.a.o

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} + 4q^{7} + q^{9} - 4q^{11} - 2q^{15} - 4q^{17} - 4q^{19} + O(q^{20})$$

## 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 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. 