Properties

Label 62790bt
Number of curves 8
Conductor 62790
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("62790.bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62790bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62790.bu7 62790bt1 [1, 0, 0, -167843570, 843125287812] [12] 19021824 \(\Gamma_0(N)\)-optimal
62790.bu6 62790bt2 [1, 0, 0, -2691000050, 53729999002500] [2, 6] 38043648  
62790.bu8 62790bt3 [1, 0, 0, 513852430, 4463105748612] [4] 57065472  
62790.bu5 62790bt4 [1, 0, 0, -2696503730, 53499182368452] [6] 76087296  
62790.bu2 62790bt5 [1, 0, 0, -43056000050, 3438730826002500] [6] 76087296  
62790.bu4 62790bt6 [1, 0, 0, -2961450050, 42276481912500] [2, 2] 114130944  
62790.bu3 62790bt7 [1, 0, 0, -18469941230, -933806241069048] [2] 228261888  
62790.bu1 62790bt8 [1, 0, 0, -43057798550, 3438429180592800] [2] 228261888  

Rank

sage: E.rank()
 

The elliptic curves in class 62790bt have rank \(0\).

Modular form 62790.2.a.bu

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} + q^{12} + q^{13} + q^{14} + q^{15} + q^{16} + 6q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.