# Properties

 Label 32487b Number of curves $2$ Conductor $32487$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 32487b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32487.c1 32487b1 $$[1, 1, 1, -22296, -1290024]$$ $$10418796526321/6390657$$ $$751854405393$$ $$$$ $$107520$$ $$1.2216$$ $$\Gamma_0(N)$$-optimal
32487.c2 32487b2 $$[1, 1, 1, -18131, -1781494]$$ $$-5602762882081/8312741073$$ $$-977985674497377$$ $$$$ $$215040$$ $$1.5682$$

## Rank

sage: E.rank()

The elliptic curves in class 32487b have rank $$0$$.

## Complex multiplication

The elliptic curves in class 32487b do not have complex multiplication.

## Modular form 32487.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} - q^{4} + 4q^{5} + q^{6} + 3q^{8} + q^{9} - 4q^{10} - 4q^{11} + q^{12} - q^{13} - 4q^{15} - q^{16} - q^{17} - q^{18} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 