# Properties

 Label 490k Number of curves 2 Conductor 490 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("490.e1")

sage: E.isogeny_class()

## Elliptic curves in class 490k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
490.e1 490k1 [1, -1, 1, -132, -549] [] 120 $$\Gamma_0(N)$$-optimal
490.e2 490k2 [1, -1, 1, 918, 5289] [7] 840

## Rank

sage: E.rank()

The elliptic curves in class 490k have rank $$0$$.

## Modular form490.2.a.e

sage: E.q_eigenform(10)

$$q + q^{2} - 3q^{3} + q^{4} + q^{5} - 3q^{6} + q^{8} + 6q^{9} + q^{10} - 2q^{11} - 3q^{12} - 3q^{15} + q^{16} + 4q^{17} + 6q^{18} + 6q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.