# Properties

 Label 286650.z Number of curves 4 Conductor 286650 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("286650.z1")

sage: E.isogeny_class()

## Elliptic curves in class 286650.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286650.z1 286650z4 [1, -1, 0, -987878817, -11950735818659]  94371840
286650.z2 286650z2 [1, -1, 0, -61778817, -186487518659] [2, 2] 47185920
286650.z3 286650z3 [1, -1, 0, -38846817, -326670834659]  94371840
286650.z4 286650z1 [1, -1, 0, -5330817, -491358659]  23592960 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 286650.2.a.z

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 