Properties

Label 283920.dk
Number of curves $8$
Conductor $283920$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("283920.dk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 283920.dk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
283920.dk1 283920dk8 [0, -1, 0, -17443560, -17636072208] [2] 31850496  
283920.dk2 283920dk5 [0, -1, 0, -15577800, -23659848720] [2] 10616832  
283920.dk3 283920dk6 [0, -1, 0, -7303560, 7397559792] [2, 2] 15925248  
283920.dk4 283920dk3 [0, -1, 0, -7249480, 7515324400] [2] 7962624  
283920.dk5 283920dk2 [0, -1, 0, -976200, -367376400] [2, 2] 5308416  
283920.dk6 283920dk4 [0, -1, 0, -219080, -923405328] [2] 10616832  
283920.dk7 283920dk1 [0, -1, 0, -110920, 5040112] [2] 2654208 \(\Gamma_0(N)\)-optimal
283920.dk8 283920dk7 [0, -1, 0, 1971160, 24893391600] [2] 31850496  

Rank

sage: E.rank()
 

The elliptic curves in class 283920.dk have rank \(2\).

Modular form 283920.2.a.dk

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.