Properties

Label 60690bu
Number of curves $6$
Conductor $60690$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("60690.bt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 60690bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
60690.bt6 60690bu1 [1, 0, 0, 2884, -83184] [2] 163840 \(\Gamma_0(N)\)-optimal
60690.bt5 60690bu2 [1, 0, 0, -20236, -864640] [2, 2] 327680  
60690.bt4 60690bu3 [1, 0, 0, -106936, 12712580] [2] 655360  
60690.bt2 60690bu4 [1, 0, 0, -303456, -64362564] [2, 2] 655360  
60690.bt3 60690bu5 [1, 0, 0, -283226, -73308270] [2] 1310720  
60690.bt1 60690bu6 [1, 0, 0, -4855206, -4118151114] [2] 1310720  

Rank

sage: E.rank()
 

The elliptic curves in class 60690bu have rank \(1\).

Modular form 60690.2.a.bt

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} - q^{7} + q^{8} + q^{9} - q^{10} - 4q^{11} + q^{12} - 2q^{13} - q^{14} - q^{15} + q^{16} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.