# Properties

 Label 86394l Number of curves $4$ Conductor $86394$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 86394l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86394.i4 86394l1 $$[1, 1, 0, 119, -134075]$$ $$103823/4386816$$ $$-7771512139776$$ $$$$ $$276480$$ $$1.1523$$ $$\Gamma_0(N)$$-optimal
86394.i3 86394l2 $$[1, 1, 0, -38601, -2883195]$$ $$3590714269297/73410624$$ $$130051398464064$$ $$[2, 2]$$ $$552960$$ $$1.4989$$
86394.i2 86394l3 $$[1, 1, 0, -82161, 4757229]$$ $$34623662831857/14438442312$$ $$25578581300689032$$ $$$$ $$1105920$$ $$1.8455$$
86394.i1 86394l4 $$[1, 1, 0, -614561, -185692899]$$ $$14489843500598257/6246072$$ $$11065297558392$$ $$$$ $$1105920$$ $$1.8455$$

## Rank

sage: E.rank()

The elliptic curves in class 86394l have rank $$1$$.

## Complex multiplication

The elliptic curves in class 86394l do not have complex multiplication.

## Modular form 86394.2.a.l

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - 2q^{5} + q^{6} + q^{7} - q^{8} + q^{9} + 2q^{10} - q^{12} + 6q^{13} - q^{14} + 2q^{15} + q^{16} - q^{17} - q^{18} + O(q^{20})$$ ## 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. 