# Properties

 Label 33640f Number of curves 2 Conductor 33640 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("33640.b1")

sage: E.isogeny_class()

## Elliptic curves in class 33640f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33640.b2 33640f1 [0, 1, 0, -251, -1610]  8960 $$\Gamma_0(N)$$-optimal
33640.b1 33640f2 [0, 1, 0, -396, 304]  17920

## Rank

sage: E.rank()

The elliptic curves in class 33640f have rank $$1$$.

## Modular form 33640.2.a.b

sage: E.q_eigenform(10)

$$q - 2q^{3} - q^{5} + q^{9} + 2q^{11} + 2q^{13} + 2q^{15} - 4q^{17} - 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 