# Properties

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

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

sage: E.isogeny_class()

## Elliptic curves in class 32487.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32487.j1 32487r2 $$[1, 0, 1, -16049, 260579]$$ $$3885442650361/1996623837$$ $$234900797799213$$ $$$$ $$207360$$ $$1.4497$$
32487.j2 32487r1 $$[1, 0, 1, -12864, 559969]$$ $$2000852317801/2094417$$ $$246406065633$$ $$$$ $$103680$$ $$1.1031$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 32487.2.a.j

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} - q^{4} + 4 q^{5} + q^{6} - 3 q^{8} + q^{9} + 4 q^{10} + 6 q^{11} - q^{12} + q^{13} + 4 q^{15} - q^{16} - q^{17} + q^{18} - 4 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 