Properties

Label 1584.n
Number of curves 4
Conductor 1584
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1584.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1584.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1584.n1 1584c4 [0, 0, 0, -6339, 194258] [4] 1536  
1584.n2 1584c3 [0, 0, 0, -939, -6838] [2] 1536  
1584.n3 1584c2 [0, 0, 0, -399, 2990] [2, 2] 768  
1584.n4 1584c1 [0, 0, 0, 6, 155] [2] 384 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1584.n have rank \(0\).

Modular form 1584.2.a.n

sage: E.q_eigenform(10)
 
\( q + 2q^{5} - 4q^{7} - q^{11} + 6q^{13} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.