Properties

Label 5390bf
Number of curves 4
Conductor 5390
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("5390.bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5390bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5390.bj3 5390bf1 [1, 1, 1, -2745, -1078393] [2] 27648 \(\Gamma_0(N)\)-optimal
5390.bj2 5390bf2 [1, 1, 1, -175225, -28054265] [2] 55296  
5390.bj4 5390bf3 [1, 1, 1, 24695, 29028775] [2] 82944  
5390.bj1 5390bf4 [1, 1, 1, -1279685, 540867487] [2] 165888  

Rank

sage: E.rank()
 

The elliptic curves in class 5390bf have rank \(0\).

Modular form 5390.2.a.bj

sage: E.q_eigenform(10)
 
\( q + q^{2} + 2q^{3} + q^{4} + q^{5} + 2q^{6} + q^{8} + q^{9} + q^{10} - q^{11} + 2q^{12} + 4q^{13} + 2q^{15} + q^{16} + q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.