Properties

Label 350658.cp
Number of curves $4$
Conductor $350658$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cp1")
 
E.isogeny_class()
 

Elliptic curves in class 350658.cp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350658.cp1 350658cp4 \([1, -1, 1, -7505411, -7912085893]\) \(36204575259448513/1527466248\) \(1972673733020610312\) \([2]\) \(13271040\) \(2.5906\)  
350658.cp2 350658cp2 \([1, -1, 1, -492251, -110646709]\) \(10214075575873/1806590016\) \(2333153138779197504\) \([2, 2]\) \(6635520\) \(2.2440\)  
350658.cp3 350658cp1 \([1, -1, 1, -143771, 19406027]\) \(254478514753/21762048\) \(28104987931840512\) \([4]\) \(3317760\) \(1.8974\) \(\Gamma_0(N)\)-optimal
350658.cp4 350658cp3 \([1, -1, 1, 945229, -636764389]\) \(72318867421247/177381135624\) \(-229082054963240827656\) \([2]\) \(13271040\) \(2.5906\)  

Rank

sage: E.rank()
 

The elliptic curves in class 350658.cp have rank \(0\).

Complex multiplication

The elliptic curves in class 350658.cp do not have complex multiplication.

Modular form 350658.2.a.cp

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 2 q^{5} - q^{7} + q^{8} - 2 q^{10} - 2 q^{13} - q^{14} + q^{16} + 2 q^{17} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.