# Properties

 Label 2016.k Number of curves $4$ Conductor $2016$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 2016.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2016.k1 2016c3 $$[0, 0, 0, -2019, 34918]$$ $$2438569736/21$$ $$7838208$$ $$$$ $$1024$$ $$0.49067$$
2016.k2 2016c2 $$[0, 0, 0, -444, -3008]$$ $$3241792/567$$ $$1693052928$$ $$$$ $$1024$$ $$0.49067$$
2016.k3 2016c1 $$[0, 0, 0, -129, 520]$$ $$5088448/441$$ $$20575296$$ $$[2, 2]$$ $$512$$ $$0.14410$$ $$\Gamma_0(N)$$-optimal
2016.k4 2016c4 $$[0, 0, 0, 141, 2410]$$ $$830584/7203$$ $$-2688505344$$ $$$$ $$1024$$ $$0.49067$$

## Rank

sage: E.rank()

The elliptic curves in class 2016.k have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2016.k do not have complex multiplication.

## Modular form2016.2.a.k

sage: E.q_eigenform(10)

$$q + 2 q^{5} - q^{7} + 4 q^{11} - 6 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 