# Properties

 Label 432.g Number of curves $3$ Conductor $432$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("432.g1")

sage: E.isogeny_class()

## Elliptic curves in class 432.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
432.g1 432e3 [0, 0, 0, -1971, 44658] [] 432
432.g2 432e1 [0, 0, 0, -51, -142] [] 48 $$\Gamma_0(N)$$-optimal
432.g3 432e2 [0, 0, 0, 189, -702] [] 144

## Rank

sage: E.rank()

The elliptic curves in class 432.g have rank $$0$$.

## Modular form432.2.a.g

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 