# Properties

 Label 86640bu Number of curves $2$ Conductor $86640$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("86640.w1")

sage: E.isogeny_class()

## Elliptic curves in class 86640bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86640.w2 86640bu1 [0, -1, 0, -37816, 156016]  737280 $$\Gamma_0(N)$$-optimal
86640.w1 86640bu2 [0, -1, 0, -426936, 107241840]  1474560

## Rank

sage: E.rank()

The elliptic curves in class 86640bu have rank $$0$$.

## Modular form 86640.2.a.w

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} + 4q^{7} + q^{9} - 6q^{11} - 4q^{13} + q^{15} + 6q^{17} + O(q^{20})$$

## 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 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. 