# Properties

 Label 86190i Number of curves 4 Conductor 86190 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("86190.a1")

sage: E.isogeny_class()

## Elliptic curves in class 86190i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86190.a4 86190i1 [1, 1, 0, 158012, 19086592]  1419264 $$\Gamma_0(N)$$-optimal
86190.a3 86190i2 [1, 1, 0, -818808, 171275148] [2, 2] 2838528
86190.a2 86190i3 [1, 1, 0, -5674178, -5081264118]  5677056
86190.a1 86190i4 [1, 1, 0, -11592558, 15183418398]  5677056

## Rank

sage: E.rank()

The elliptic curves in class 86190i have rank $$0$$.

## Modular form 86190.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 4q^{7} - q^{8} + q^{9} + q^{10} - 4q^{11} - q^{12} + 4q^{14} + q^{15} + q^{16} + q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 