# Properties

 Label 160016a Number of curves $2$ Conductor $160016$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("160016.a1")

sage: E.isogeny_class()

## Elliptic curves in class 160016a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
160016.a2 160016a1 [0, 0, 0, -857507, -305635870]  1492992 $$\Gamma_0(N)$$-optimal
160016.a1 160016a2 [0, 0, 0, -863347, -301261710]  2985984

## Rank

sage: E.rank()

The elliptic curves in class 160016a have rank $$0$$.

## Modular form 160016.2.a.a

sage: E.q_eigenform(10)

$$q - 4q^{5} + 4q^{7} - 3q^{9} - 4q^{11} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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. 