Properties

Label 156702.bu
Number of curves $2$
Conductor $156702$
CM no
Rank $1$
Graph

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

Elliptic curves in class 156702.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
156702.bu1 156702bg1 \([1, 1, 1, -7634495, -8124541531]\) \(-418288977642645996769/122877464621184\) \(-14456410835217676416\) \([]\) \(6322176\) \(2.6555\) \(\Gamma_0(N)\)-optimal
156702.bu2 156702bg2 \([1, 1, 1, 42364615, 358508096729]\) \(71473535169369644529791/513262758348672548034\) \(-60384850256962976603652066\) \([]\) \(44255232\) \(3.6285\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 156702.bu do not have complex multiplication.

Modular form 156702.2.a.bu

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.