# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("86190.l1")

sage: E.isogeny_class()

## Elliptic curves in class 86190g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86190.l3 86190g1 [1, 1, 0, -545873, 85325973]  3096576 $$\Gamma_0(N)$$-optimal
86190.l2 86190g2 [1, 1, 0, -4006993, -3028989803] [2, 2] 6193152
86190.l4 86190g3 [1, 1, 0, 373487, -9292200107]  12386304
86190.l1 86190g4 [1, 1, 0, -63765393, -196012766763]  12386304

## Rank

sage: E.rank()

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

## Modular form 86190.2.a.l

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 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. 