# Properties

 Label 4032g Number of curves $4$ Conductor $4032$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 4032g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4032.bb4 4032g1 [0, 0, 0, 36, -432]  1024 $$\Gamma_0(N)$$-optimal
4032.bb3 4032g2 [0, 0, 0, -684, -6480] [2, 2] 2048
4032.bb1 4032g3 [0, 0, 0, -10764, -429840]  4096
4032.bb2 4032g4 [0, 0, 0, -2124, 29808]  4096

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4032.2.a.g

sage: E.q_eigenform(10)

$$q + 2q^{5} - q^{7} - 4q^{11} - 2q^{13} + 6q^{17} - 8q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 