# Properties

 Label 8016f Number of curves $2$ Conductor $8016$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 8016f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8016.f2 8016f1 $$[0, -1, 0, -72, 1008]$$ $$-10218313/96192$$ $$-394002432$$ $$$$ $$3456$$ $$0.33172$$ $$\Gamma_0(N)$$-optimal
8016.f1 8016f2 $$[0, -1, 0, -1992, 34800]$$ $$213525509833/669336$$ $$2741600256$$ $$$$ $$6912$$ $$0.67830$$

## Rank

sage: E.rank()

The elliptic curves in class 8016f have rank $$0$$.

## Complex multiplication

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

## Modular form8016.2.a.f

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} + 4q^{7} + q^{9} + 4q^{11} - 2q^{15} - 4q^{17} + 4q^{19} + O(q^{20})$$ ## 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. 