# Properties

 Label 8036.d Number of curves $2$ Conductor $8036$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 8036.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8036.d1 8036a1 $$[0, 1, 0, -2172, 40004]$$ $$-768208/41$$ $$-60507351296$$ $$$$ $$8064$$ $$0.82776$$ $$\Gamma_0(N)$$-optimal
8036.d2 8036a2 $$[0, 1, 0, 11548, 89396]$$ $$115393712/68921$$ $$-101712857528576$$ $$[]$$ $$24192$$ $$1.3771$$

## Rank

sage: E.rank()

The elliptic curves in class 8036.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 8036.d do not have complex multiplication.

## Modular form8036.2.a.d

sage: E.q_eigenform(10)

$$q + q^{3} - 3q^{5} - 2q^{9} + 3q^{11} - 4q^{13} - 3q^{15} - 7q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 