# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("33640.h1")

sage: E.isogeny_class()

## Elliptic curves in class 33640b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33640.h2 33640b1 [0, -1, 0, -211371, -37153480]  259840 $$\Gamma_0(N)$$-optimal
33640.h1 33640b2 [0, -1, 0, -333316, 10746516]  519680

## Rank

sage: E.rank()

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

## Modular form 33640.2.a.h

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. 