# Properties

 Label 4032.d Number of curves $2$ Conductor $4032$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 4032.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4032.d1 4032p2 $$[0, 0, 0, -1452, 21040]$$ $$3543122/49$$ $$4682022912$$ $$$$ $$3072$$ $$0.66121$$
4032.d2 4032p1 $$[0, 0, 0, -12, 880]$$ $$-4/7$$ $$-334430208$$ $$$$ $$1536$$ $$0.31464$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4032.d have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4032.d do not have complex multiplication.

## Modular form4032.2.a.d

sage: E.q_eigenform(10)

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