# Properties

 Label 490245.bq Number of curves 2 Conductor 490245 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("490245.bq1")
sage: E.isogeny_class()

## Elliptic curves in class 490245.bq

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
490245.bq1 490245bq1 [1, 1, 0, -18302, -960609] 2 663552 $$\Gamma_0(N)$$-optimal
490245.bq2 490245bq2 [1, 1, 0, -17077, -1093154] 2 1327104

## Rank

sage: E.rank()

The elliptic curves in class 490245.bq have rank $$0$$.

## Modular form 490245.2.a.bq

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

## 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. 