# Properties

 Label 32490.bl Number of curves $4$ Conductor $32490$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("32490.bl1")

sage: E.isogeny_class()

## Elliptic curves in class 32490.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
32490.bl1 32490bp4 [1, -1, 1, -9877028, 11950257597]  1105920
32490.bl2 32490bp3 [1, -1, 1, -714848, 123949581]  1105920
32490.bl3 32490bp2 [1, -1, 1, -617378, 186798237] [2, 2] 552960
32490.bl4 32490bp1 [1, -1, 1, -32558, 3866541]  276480 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 32490.2.a.bl

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + 4q^{7} + q^{8} - q^{10} + 4q^{11} + 2q^{13} + 4q^{14} + q^{16} + 2q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 