# Properties

 Label 40432.b Number of curves 6 Conductor 40432 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("40432.b1")

sage: E.isogeny_class()

## Elliptic curves in class 40432.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40432.b1 40432r6 [0, 1, 0, -15771488, -24113032076] [2] 1026432
40432.b2 40432r5 [0, 1, 0, -984928, -377645964] [2] 513216
40432.b3 40432r4 [0, 1, 0, -205168, -29387820] [2] 342144
40432.b4 40432r2 [0, 1, 0, -60768, 5741812] [2] 114048
40432.b5 40432r1 [0, 1, 0, -3008, 127540] [2] 57024 $$\Gamma_0(N)$$-optimal
40432.b6 40432r3 [0, 1, 0, 25872, -2679596] [2] 171072

## Rank

sage: E.rank()

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

## Modular form 40432.2.a.b

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.