# Properties

 Label 33640.a Number of curves 2 Conductor 33640 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33640.a1")

sage: E.isogeny_class()

## Elliptic curves in class 33640.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33640.a1 33640e2 [0, 1, 0, -568796, -165191120]  322560
33640.a2 33640e1 [0, 1, 0, -43171, -1406370]  161280 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 33640.a have rank $$0$$.

## Modular form 33640.2.a.a

sage: E.q_eigenform(10)

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

## 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. 