# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("86640.d1")

sage: E.isogeny_class()

## Elliptic curves in class 86640bq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86640.d2 86640bq1 [0, -1, 0, -1305496, -590710544]  1751040 $$\Gamma_0(N)$$-optimal
86640.d1 86640bq2 [0, -1, 0, -21059416, -37190773520]  3502080

## Rank

sage: E.rank()

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

## Modular form 86640.2.a.d

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - 2q^{7} + q^{9} + 2q^{13} + q^{15} - 6q^{17} + O(q^{20})$$

## 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. 