Properties

Label 37026.bk
Number of curves 4
Conductor 37026
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("37026.bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37026.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37026.bk1 37026ba4 [1, -1, 1, -123080, -11454055] [2] 311040  
37026.bk2 37026ba3 [1, -1, 1, -112190, -14433559] [2] 155520  
37026.bk3 37026ba2 [1, -1, 1, -46850, 3913913] [2] 103680  
37026.bk4 37026ba1 [1, -1, 1, -3290, 45785] [2] 51840 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37026.bk have rank \(0\).

Modular form 37026.2.a.bk

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + 4q^{7} + q^{8} - 2q^{13} + 4q^{14} + q^{16} - q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.