Properties

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

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Show commands: SageMath
E = EllipticCurve("cs1")
 
E.isogeny_class()
 

Elliptic curves in class 140790cs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
140790.c2 140790cs1 \([1, 1, 0, 89882, 238152772]\) \(248858189/76050000\) \(-24540399416092950000\) \([2]\) \(4377600\) \(2.3997\) \(\Gamma_0(N)\)-optimal
140790.c1 140790cs2 \([1, 1, 0, -5260138, 4517098768]\) \(49880735279731/1523437500\) \(491594539585195312500\) \([2]\) \(8755200\) \(2.7463\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 140790.2.a.cs

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.