Properties

Label 283920d
Number of curves 8
Conductor 283920
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("283920.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 283920d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
283920.d7 283920d1 [0, -1, 0, 567784, -124275984] [2] 7077888 \(\Gamma_0(N)\)-optimal
283920.d6 283920d2 [0, -1, 0, -2893336, -1110002960] [2, 2] 14155776  
283920.d5 283920d3 [0, -1, 0, -20415256, 34718819056] [2, 2] 28311552  
283920.d4 283920d4 [0, -1, 0, -40749336, -100080729360] [2] 28311552  
283920.d2 283920d5 [0, -1, 0, -324615256, 2251241699056] [2, 2] 56623104  
283920.d8 283920d6 [0, -1, 0, 3434024, 110960197360] [2] 56623104  
283920.d1 283920d7 [0, -1, 0, -5193843256, 144074324118256] [2] 113246208  
283920.d3 283920d8 [0, -1, 0, -322587256, 2280756399856] [2] 113246208  

Rank

sage: E.rank()
 

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

Modular form 283920.2.a.d

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 2 & 2 \\ 8 & 4 & 2 & 8 & 4 & 1 & 8 & 8 \\ 16 & 8 & 4 & 16 & 2 & 8 & 1 & 4 \\ 16 & 8 & 4 & 16 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.