Properties

Label 283920.bp
Number of curves 8
Conductor 283920
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("283920.bp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 283920.bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
283920.bp1 283920bp7 [0, -1, 0, -108674990376, 13789346035420656] [2] 445906944  
283920.bp2 283920bp6 [0, -1, 0, -6792191176, 215459944884976] [2, 2] 222953472  
283920.bp3 283920bp8 [0, -1, 0, -6708718696, 221013602702320] [2] 445906944  
283920.bp4 283920bp4 [0, -1, 0, -1342279176, 18897685672176] [2] 148635648  
283920.bp5 283920bp3 [0, -1, 0, -429733256, 3279608202480] [2] 111476736  
283920.bp6 283920bp2 [0, -1, 0, -111959176, 80679464176] [2, 2] 74317824  
283920.bp7 283920bp1 [0, -1, 0, -69560456, -222081315600] [2] 37158912 \(\Gamma_0(N)\)-optimal
283920.bp8 283920bp5 [0, -1, 0, 439981304, 639684782320] [2] 148635648  

Rank

sage: E.rank()
 

The elliptic curves in class 283920.bp have rank \(1\).

Modular form 283920.2.a.bp

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{7} + q^{9} + q^{15} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.