# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 8016.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8016.d1 8016c2 $$[0, -1, 0, -5128, 143008]$$ $$14566408766500/6777027$$ $$6939675648$$ $$$$ $$7040$$ $$0.84463$$
8016.d2 8016c1 $$[0, -1, 0, -268, 3040]$$ $$-8346562000/9861183$$ $$-2524462848$$ $$$$ $$3520$$ $$0.49806$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8016.2.a.d

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} + 4q^{11} + 2q^{13} + 4q^{19} + O(q^{20})$$ ## 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. 