# Properties

 Label 140790.u Number of curves $2$ Conductor $140790$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 140790.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
140790.u1 140790ch2 $$[1, 0, 1, -16614, 736966]$$ $$10779215329/1232010$$ $$57960995850810$$ $$$$ $$628992$$ $$1.3732$$
140790.u2 140790ch1 $$[1, 0, 1, 1436, 58286]$$ $$6967871/35100$$ $$-1651310423100$$ $$$$ $$314496$$ $$1.0266$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 140790.u have rank $$0$$.

## Complex multiplication

The elliptic curves in class 140790.u do not have complex multiplication.

## Modular form 140790.2.a.u

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 2q^{7} - q^{8} + q^{9} + q^{10} + 4q^{11} + q^{12} + q^{13} - 2q^{14} - q^{15} + q^{16} + 8q^{17} - q^{18} + O(q^{20})$$ ## 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. 