# Properties

 Label 160446a Number of curves $2$ Conductor $160446$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 160446a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160446.bg1 160446a1 $$[1, 0, 0, -4774360, -3439036864]$$ $$6793805286030262681/1048227429629952$$ $$1856998833462667395072$$ $$$$ $$18063360$$ $$2.8045$$ $$\Gamma_0(N)$$-optimal
160446.bg2 160446a2 $$[1, 0, 0, 8313000, -18973733184]$$ $$35862531227445945959/108547797844556928$$ $$-192299045297301115924608$$ $$$$ $$36126720$$ $$3.1511$$

## Rank

sage: E.rank()

The elliptic curves in class 160446a have rank $$0$$.

## Complex multiplication

The elliptic curves in class 160446a do not have complex multiplication.

## Modular form 160446.2.a.a

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} - 4q^{5} + q^{6} + 2q^{7} + q^{8} + q^{9} - 4q^{10} + q^{12} + q^{13} + 2q^{14} - 4q^{15} + q^{16} + q^{17} + q^{18} + 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 