# Properties

 Label 32490.w Number of curves $2$ Conductor $32490$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

## Elliptic curves in class 32490.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.w1 32490q2 $$[1, -1, 0, -32814, 2296120]$$ $$781484460931/900$$ $$4500189900$$ $$[2]$$ $$61440$$ $$1.1363$$
32490.w2 32490q1 $$[1, -1, 0, -2034, 36868]$$ $$-186169411/6480$$ $$-32401367280$$ $$[2]$$ $$30720$$ $$0.78973$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 32490.w have rank $$1$$.

## Complex multiplication

The elliptic curves in class 32490.w do not have complex multiplication.

## Modular form 32490.2.a.w

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} + 2 q^{7} - q^{8} - q^{10} - 2 q^{13} - 2 q^{14} + q^{16} + 6 q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.