# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("86190.e1")

sage: E.isogeny_class()

## Elliptic curves in class 86190j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86190.e1 86190j1 [1, 1, 0, -198, -1152]  24576 $$\Gamma_0(N)$$-optimal
86190.e2 86190j2 [1, 1, 0, -68, -2478]  49152

## Rank

sage: E.rank()

The elliptic curves in class 86190j have rank $$2$$.

## Modular form 86190.2.a.e

sage: E.q_eigenform(10)

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

## 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. 