Properties

Label 283920.gm
Number of curves $4$
Conductor $283920$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("gm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 283920.gm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
283920.gm1 283920gm4 [0, 1, 0, -1010000, -391024620] [2] 3538944  
283920.gm2 283920gm2 [0, 1, 0, -63600, -6029100] [2, 2] 1769472  
283920.gm3 283920gm1 [0, 1, 0, -9520, 222548] [2] 884736 \(\Gamma_0(N)\)-optimal
283920.gm4 283920gm3 [0, 1, 0, 17520, -20273772] [2] 3538944  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 283920.gm do not have complex multiplication.

Modular form 283920.2.a.gm

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} - q^{7} + q^{9} - 4q^{11} + q^{15} - 6q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.