# Properties

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

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 490e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
490.g2 490e1 $$[1, 0, 0, -1, -15]$$ $$-49/40$$ $$-96040$$ $$[3]$$ $$60$$ $$-0.36492$$ $$\Gamma_0(N)$$-optimal
490.g1 490e2 $$[1, 0, 0, -491, -4229]$$ $$-5452947409/250$$ $$-600250$$ $$[]$$ $$180$$ $$0.18439$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 490e do not have complex multiplication.

## Modular form490.2.a.e

sage: E.q_eigenform(10)

$$q + q^{2} - 2q^{3} + q^{4} - q^{5} - 2q^{6} + q^{8} + q^{9} - q^{10} + 3q^{11} - 2q^{12} + 5q^{13} + 2q^{15} + q^{16} + 6q^{17} + q^{18} - q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.