# Properties

 Label 286650d Number of curves 2 Conductor 286650 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("286650.d1")

sage: E.isogeny_class()

## Elliptic curves in class 286650d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286650.d2 286650d1 [1, -1, 0, -3809367, -20409255959]  40550400 $$\Gamma_0(N)$$-optimal
286650.d1 286650d2 [1, -1, 0, -137763117, -619316472209]  81100800

## Rank

sage: E.rank()

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

## Modular form 286650.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{8} - 6q^{11} - q^{13} + q^{16} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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. 