Properties

Label 156702bg
Number of curves 2
Conductor 156702
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("156702.bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 156702bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
156702.bu1 156702bg1 [1, 1, 1, -7634495, -8124541531] [] 6322176 \(\Gamma_0(N)\)-optimal
156702.bu2 156702bg2 [1, 1, 1, 42364615, 358508096729] [] 44255232  

Rank

sage: E.rank()
 

The elliptic curves in class 156702bg have rank \(1\).

Modular form 156702.2.a.bu

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - 2q^{11} - q^{12} + q^{13} - q^{15} + q^{16} - 4q^{17} + q^{18} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.