# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 432.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
432.g1 432e3 $$[0, 0, 0, -1971, 44658]$$ $$-1167051/512$$ $$-371504185344$$ $$[]$$ $$432$$ $$0.92725$$
432.g2 432e1 $$[0, 0, 0, -51, -142]$$ $$-132651/2$$ $$-221184$$ $$[]$$ $$48$$ $$-0.17136$$ $$\Gamma_0(N)$$-optimal
432.g3 432e2 $$[0, 0, 0, 189, -702]$$ $$9261/8$$ $$-644972544$$ $$[]$$ $$144$$ $$0.37794$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 432.g do not have complex multiplication.

## Modular form432.2.a.g

sage: E.q_eigenform(10)

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