# Properties

 Label 286110cw Number of curves 2 Conductor 286110 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("286110.cw1")

sage: E.isogeny_class()

## Elliptic curves in class 286110cw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286110.cw2 286110cw1 [1, -1, 0, -2288934, -586452812]  12386304 $$\Gamma_0(N)$$-optimal
286110.cw1 286110cw2 [1, -1, 0, -30587814, -65068280780]  24772608

## Rank

sage: E.rank()

The elliptic curves in class 286110cw have rank $$1$$.

## Modular form 286110.2.a.cw

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} + 2q^{7} - q^{8} - q^{10} - q^{11} - 4q^{13} - 2q^{14} + q^{16} - 6q^{19} + O(q^{20})$$

## 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. 