# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("32490.by1")

sage: E.isogeny_class()

## Elliptic curves in class 32490.by

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
32490.by1 32490br2 [1, -1, 1, -11845922, -15689857579]  1167360
32490.by2 32490br1 [1, -1, 1, -734342, -249206011]  583680 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 32490.2.a.by

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 