Properties

Label 283920ej
Number of curves $6$
Conductor $283920$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("283920.ej1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 283920ej

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
283920.ej4 283920ej1 [0, 1, 0, -29631, -1973100] [2] 589824 \(\Gamma_0(N)\)-optimal
283920.ej3 283920ej2 [0, 1, 0, -30476, -1855476] [2, 2] 1179648  
283920.ej2 283920ej3 [0, 1, 0, -114976, 12982724] [2, 2] 2359296  
283920.ej5 283920ej4 [0, 1, 0, 40504, -9152220] [2] 2359296  
283920.ej1 283920ej5 [0, 1, 0, -1771176, 906668244] [2] 4718592  
283920.ej6 283920ej6 [0, 1, 0, 189224, 70294004] [2] 4718592  

Rank

sage: E.rank()
 

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

Modular form 283920.2.a.ej

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.