# Properties

 Label 40432j Number of curves $4$ Conductor $40432$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 40432j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40432.l4 40432j1 [0, 0, 0, 361, 13718]  24192 $$\Gamma_0(N)$$-optimal
40432.l3 40432j2 [0, 0, 0, -6859, 205770] [2, 2] 48384
40432.l2 40432j3 [0, 0, 0, -21299, -946542]  96768
40432.l1 40432j4 [0, 0, 0, -107939, 13649410]  96768

## Rank

sage: E.rank()

The elliptic curves in class 40432j have rank $$1$$.

## Complex multiplication

The elliptic curves in class 40432j do not have complex multiplication.

## Modular form 40432.2.a.j

sage: E.q_eigenform(10)

$$q + 2q^{5} + q^{7} - 3q^{9} + 4q^{11} - 2q^{13} - 6q^{17} + O(q^{20})$$

## 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. 