# Properties

 Label 86190.b Number of curves 4 Conductor 86190 CM no Rank 1 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("86190.b1")

sage: E.isogeny_class()

## Elliptic curves in class 86190.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86190.b1 86190c4 [1, 1, 0, -12948783, 17898665517] [2] 7741440
86190.b2 86190c3 [1, 1, 0, -10853183, -13695181443] [2] 7741440
86190.b3 86190c2 [1, 1, 0, -1084983, 72119637] [2, 2] 3870720
86190.b4 86190c1 [1, 1, 0, 267017, 9116437] [2] 1935360 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 86190.2.a.b

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.