Properties

Label 54150.bj
Number of curves 8
Conductor 54150
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("54150.bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54150.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54150.bj1 54150bb7 [1, 0, 1, -48135026, 128536469948] [2] 3981312  
54150.bj2 54150bb8 [1, 0, 1, -4093026, 433453948] [2] 3981312  
54150.bj3 54150bb6 [1, 0, 1, -3010026, 2005969948] [2, 2] 1990656  
54150.bj4 54150bb5 [1, 0, 1, -2603901, -1617477302] [2] 1327104  
54150.bj5 54150bb4 [1, 0, 1, -618401, 161169698] [2] 1327104  
54150.bj6 54150bb2 [1, 0, 1, -167151, -23842802] [2, 2] 663552  
54150.bj7 54150bb3 [1, 0, 1, -122026, 53681948] [2] 995328  
54150.bj8 54150bb1 [1, 0, 1, 13349, -1821802] [2] 331776 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 54150.bj have rank \(1\).

Modular form 54150.2.a.bj

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.