# Properties

 Label 1586.c Number of curves 2 Conductor 1586 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1586.c1")
sage: E.isogeny_class()

## Elliptic curves in class 1586.c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1586.c1 1586d2 [1, 1, 1, -3492955, -2647300407] 1 47000
1586.c2 1586d1 [1, 1, 1, 16005, 10336393] 5 9400 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1586.c have rank $$0$$.

## Modular form1586.2.a.c

sage: E.q_eigenform(10)
$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + 3q^{7} + q^{8} - 2q^{9} + q^{10} + 2q^{11} - q^{12} + q^{13} + 3q^{14} - q^{15} + q^{16} + 3q^{17} - 2q^{18} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.