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Properties

Label 140790cg
Number of curves $2$
Conductor $140790$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("cg1")
 
E.isogeny_class()
 

Elliptic curves in class 140790cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
140790.t1 140790cg1 \([1, 0, 1, -6734824, 6726701246]\) \(-1989177620032729/4928040\) \(-83695678008569640\) \([3]\) \(4727808\) \(2.4863\) \(\Gamma_0(N)\)-optimal
140790.t2 140790cg2 \([1, 0, 1, -4574239, 11111824562]\) \(-623234268729289/2780241984000\) \(-47218415004498913344000\) \([]\) \(14183424\) \(3.0356\)  

Rank

sage: E.rank()
 

The elliptic curves in class 140790cg have rank \(1\).

Complex multiplication

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

Modular form 140790.2.a.cg

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + q^{10} + 3 q^{11} + q^{12} + q^{13} + q^{14} - q^{15} + q^{16} - q^{18} + O(q^{20})\) Copy content 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 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.