# Properties

 Label 8016.e Number of curves $2$ Conductor $8016$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 8016.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8016.e1 8016a2 $$[0, -1, 0, -328, -1904]$$ $$1911343250/251001$$ $$514050048$$ $$$$ $$2560$$ $$0.39962$$
8016.e2 8016a1 $$[0, -1, 0, 32, -176]$$ $$3429500/13527$$ $$-13851648$$ $$$$ $$1280$$ $$0.053043$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8016.e have rank $$1$$.

## Complex multiplication

The elliptic curves in class 8016.e do not have complex multiplication.

## Modular form8016.2.a.e

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} + 2q^{17} + 8q^{19} + O(q^{20})$$ ## 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. 