# Properties

 Label 32490.by Number of curves $2$ Conductor $32490$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("by1")

sage: E.isogeny_class()

## Elliptic curves in class 32490.by

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32490.by1 32490br2 $$[1, -1, 1, -11845922, -15689857579]$$ $$781484460931/900$$ $$211715398512801900$$ $$$$ $$1167360$$ $$2.6085$$
32490.by2 32490br1 $$[1, -1, 1, -734342, -249206011]$$ $$-186169411/6480$$ $$-1524350869292173680$$ $$$$ $$583680$$ $$2.2620$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 32490.by have rank $$0$$.

## Complex multiplication

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

## Modular form 32490.2.a.by

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. 