# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

## Elliptic curves in class 160446.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
160446.z1 160446v1 $$[1, 1, 1, -365483, 77202137]$$ $$3047678972871625/304559880768$$ $$539546406933238848$$ $$$$ $$2580480$$ $$2.1388$$ $$\Gamma_0(N)$$-optimal
160446.z2 160446v2 $$[1, 1, 1, 452477, 374612393]$$ $$5783051584712375/37533175779528$$ $$-66492310417156403208$$ $$$$ $$5160960$$ $$2.4854$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 160446.2.a.z

sage: E.q_eigenform(10)

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