Properties

Label 9702.bu
Number of curves 4
Conductor 9702
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("9702.bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 9702.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
9702.bu1 9702ca3 [1, -1, 1, -35510, -2556795] [2] 34560  
9702.bu2 9702ca4 [1, -1, 1, -17870, -5111067] [2] 69120  
9702.bu3 9702ca1 [1, -1, 1, -2435, 44223] [2] 11520 \(\Gamma_0(N)\)-optimal
9702.bu4 9702ca2 [1, -1, 1, 1975, 183579] [2] 23040  

Rank

sage: E.rank()
 

The elliptic curves in class 9702.bu have rank \(1\).

Modular form 9702.2.a.bu

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

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.