# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("286650.c1")

sage: E.isogeny_class()

## Elliptic curves in class 286650.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286650.c1 286650c1 [1, -1, 0, -1086192, -422887284]  8847360 $$\Gamma_0(N)$$-optimal
286650.c2 286650c2 [1, -1, 0, 347058, -1459127034]  17694720

## Rank

sage: E.rank()

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

## Modular form 286650.2.a.c

sage: E.q_eigenform(10)

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

## 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 LMFDB 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 LMFDB labels. 