# Properties

 Label 4032.u Number of curves 4 Conductor 4032 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4032.u1")

sage: E.isogeny_class()

## Elliptic curves in class 4032.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4032.u1 4032n4 [0, 0, 0, -65820, 6499568]  9216
4032.u2 4032n3 [0, 0, 0, -4080, 103304]  4608
4032.u3 4032n2 [0, 0, 0, -1020, 4016]  3072
4032.u4 4032n1 [0, 0, 0, 240, 488]  1536 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form4032.2.a.u

sage: E.q_eigenform(10)

$$q + q^{7} - 6q^{11} - 2q^{13} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 