Properties

Label 142296.br
Number of curves 4
Conductor 142296
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("142296.br1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 142296.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
142296.br1 142296bo3 [0, -1, 0, -4175992, 3286028572] [2] 3317760  
142296.br2 142296bo4 [0, -1, 0, -618592, -115415012] [2] 3317760  
142296.br3 142296bo2 [0, -1, 0, -262852, 50644420] [2, 2] 1658880  
142296.br4 142296bo1 [0, -1, 0, 3953, 2619520] [2] 829440 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 142296.br have rank \(0\).

Modular form 142296.2.a.br

sage: E.q_eigenform(10)
 
\( q - q^{3} + 2q^{5} + q^{9} + 6q^{13} - 2q^{15} + 6q^{17} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.