Properties

Label 283920gf
Number of curves $6$
Conductor $283920$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("283920.gf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 283920gf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
283920.gf6 283920gf1 [0, 1, 0, 26984, 2396564] [2] 1769472 \(\Gamma_0(N)\)-optimal
283920.gf5 283920gf2 [0, 1, 0, -189336, 24634260] [2, 2] 3538944  
283920.gf2 283920gf3 [0, 1, 0, -2839256, 1840359444] [2, 2] 7077888  
283920.gf4 283920gf4 [0, 1, 0, -1000536, -364417260] [2] 7077888  
283920.gf1 283920gf5 [0, 1, 0, -45427256, 117833036244] [2] 14155776  
283920.gf3 283920gf6 [0, 1, 0, -2649976, 2096493140] [2] 14155776  

Rank

sage: E.rank()
 

The elliptic curves in class 283920gf have rank \(0\).

Modular form 283920.2.a.gf

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} + q^{7} + q^{9} + 4q^{11} - q^{15} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.