# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("62866.c1")

sage: E.isogeny_class()

## Elliptic curves in class 62866a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62866.c2 62866a1 [1, -1, 0, -110, -428] [] 10584 $$\Gamma_0(N)$$-optimal
62866.c1 62866a2 [1, -1, 0, -1400, 62954] [] 74088

## Rank

sage: E.rank()

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

## Modular form 62866.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} + 3q^{7} - q^{8} - 3q^{9} + q^{10} - 2q^{11} + 2q^{13} - 3q^{14} + q^{16} - q^{17} + 3q^{18} - q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 