# Properties

 Label 62866b Number of curves $2$ Conductor $62866$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("62866.b1")

sage: E.isogeny_class()

## Elliptic curves in class 62866b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62866.b2 62866b1 [1, -1, 0, -106664, 13157744]  532224 $$\Gamma_0(N)$$-optimal
62866.b1 62866b2 [1, -1, 0, -1696804, 851161524]  1064448

## Rank

sage: E.rank()

The elliptic curves in class 62866b have rank $$0$$.

## Modular form 62866.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 4q^{5} - q^{8} - 3q^{9} + 4q^{10} - 2q^{11} + 2q^{13} + q^{16} - q^{17} + 3q^{18} - 4q^{19} + O(q^{20})$$

## 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. 