Properties

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

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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 \([1, 0, 1, -16614, 736966]\) \(10779215329/1232010\) \(57960995850810\) \([2]\) \(628992\) \(1.3732\)  
140790.u2 140790ch1 \([1, 0, 1, 1436, 58286]\) \(6967871/35100\) \(-1651310423100\) \([2]\) \(314496\) \(1.0266\) \(\Gamma_0(N)\)-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)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 2q^{7} - q^{8} + q^{9} + q^{10} + 4q^{11} + q^{12} + q^{13} - 2q^{14} - q^{15} + q^{16} + 8q^{17} - q^{18} + O(q^{20})\)  Toggle raw display

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.