# Properties

 Label 4032.i Number of curves 2 Conductor 4032 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4032.i1")

sage: E.isogeny_class()

## Elliptic curves in class 4032.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4032.i1 4032u1 [0, 0, 0, -216, 1080]  1536 $$\Gamma_0(N)$$-optimal
4032.i2 4032u2 [0, 0, 0, 324, 5616]  3072

## Rank

sage: E.rank()

The elliptic curves in class 4032.i have rank $$0$$.

## Modular form4032.2.a.i

sage: E.q_eigenform(10)

$$q - 2q^{5} - q^{7} + 6q^{11} + 6q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 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. 