# Properties

 Label 286110.ez Number of curves $2$ Conductor $286110$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ez1")

sage: E.isogeny_class()

## Elliptic curves in class 286110.ez

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286110.ez1 286110ez2 [1, -1, 1, -373298, -55981969]  4718592
286110.ez2 286110ez1 [1, -1, 1, 68872, -6105193]  2359296 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 286110.ez have rank $$0$$.

## Complex multiplication

The elliptic curves in class 286110.ez do not have complex multiplication.

## Modular form 286110.2.a.ez

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + 2q^{7} + q^{8} - q^{10} + q^{11} + 2q^{14} + q^{16} + O(q^{20})$$

## 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. 