# Properties

 Label 286650x Number of curves 2 Conductor 286650 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("286650.x1")

sage: E.isogeny_class()

## Elliptic curves in class 286650x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286650.x2 286650x1 [1, -1, 0, -579042, -178347884]  5529600 $$\Gamma_0(N)$$-optimal
286650.x1 286650x2 [1, -1, 0, -9399042, -11088687884]  11059200

## Rank

sage: E.rank()

The elliptic curves in class 286650x have rank $$1$$.

## Modular form 286650.2.a.x

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} - 4q^{11} - q^{13} + q^{16} - 4q^{17} + 2q^{19} + O(q^{20})$$

## 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. 