Properties

Label 37026bj
Number of curves 6
Conductor 37026
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("37026.bm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37026bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37026.bm5 37026bj1 [1, -1, 1, -37049, 2554841] [2] 163840 \(\Gamma_0(N)\)-optimal
37026.bm4 37026bj2 [1, -1, 1, -124169, -13858567] [2, 2] 327680  
37026.bm6 37026bj3 [1, -1, 1, 246091, -80949679] [2] 655360  
37026.bm2 37026bj4 [1, -1, 1, -1888349, -998271007] [2, 2] 655360  
37026.bm3 37026bj5 [1, -1, 1, -1790339, -1106591659] [2] 1310720  
37026.bm1 37026bj6 [1, -1, 1, -30213239, -63913516675] [2] 1310720  

Rank

sage: E.rank()
 

The elliptic curves in class 37026bj have rank \(1\).

Modular form 37026.2.a.bm

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + 2q^{5} + q^{8} + 2q^{10} + 2q^{13} + q^{16} + q^{17} - 4q^{19} + O(q^{20}) \)

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 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.