# Properties

 Label 286650.j Number of curves 4 Conductor 286650 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("286650.j1")

sage: E.isogeny_class()

## Elliptic curves in class 286650.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286650.j1 286650j3 [1, -1, 0, -567495567, -5203311064659]  95551488
286650.j2 286650j4 [1, -1, 0, -564408567, -5262720379659]  191102976
286650.j3 286650j1 [1, -1, 0, -8362692, -4177561284]  31850496 $$\Gamma_0(N)$$-optimal
286650.j4 286650j2 [1, -1, 0, 29453058, -31518348534]  63700992

## Rank

sage: E.rank()

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

## Modular form 286650.2.a.j

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 