# Properties

 Label 86190s Number of curves 2 Conductor 86190 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("86190.q1")

sage: E.isogeny_class()

## Elliptic curves in class 86190s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86190.q1 86190s1 [1, 1, 0, -3487, -80699]  64512 $$\Gamma_0(N)$$-optimal
86190.q2 86190s2 [1, 1, 0, -2967, -104931]  129024

## Rank

sage: E.rank()

The elliptic curves in class 86190s have rank $$1$$.

## Modular form 86190.2.a.q

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{8} + q^{9} - q^{10} + 2q^{11} - q^{12} - q^{15} + q^{16} - q^{17} - q^{18} + 2q^{19} + O(q^{20})$$

## 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. 