# Properties

 Label 134640.bw Number of curves 2 Conductor 134640 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("134640.bw1")

sage: E.isogeny_class()

## Elliptic curves in class 134640.bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
134640.bw1 134640ci2 [0, 0, 0, -1693443, 847722242]  2064384
134640.bw2 134640ci1 [0, 0, 0, -126723, 7646978]  1032192 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 134640.bw have rank $$1$$.

## Modular form 134640.2.a.bw

sage: E.q_eigenform(10)

$$q - q^{5} + 2q^{7} - q^{11} - 4q^{13} - q^{17} + 6q^{19} + O(q^{20})$$

## 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 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. 