# Properties

 Label 286650be Number of curves 2 Conductor 286650 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("286650.be1")

sage: E.isogeny_class()

## Elliptic curves in class 286650be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286650.be2 286650be1 [1, -1, 0, 328683, 8563841] [2] 4423680 $$\Gamma_0(N)$$-optimal
286650.be1 286650be2 [1, -1, 0, -1325067, 69752591] [2] 8847360

## Rank

sage: E.rank()

The elliptic curves in class 286650be have rank $$0$$.

## Modular form 286650.2.a.be

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} - 4q^{11} - q^{13} + q^{16} + 6q^{17} + O(q^{20})$$

## 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.