Properties

Label 97020.cu
Number of curves 4
Conductor 97020
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("97020.cu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 97020.cu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
97020.cu1 97020cv4 [0, 0, 0, -3131247, -2132671786] [2] 1492992  
97020.cu2 97020cv3 [0, 0, 0, -196392, -33076519] [2] 746496  
97020.cu3 97020cv2 [0, 0, 0, -44247, -2024386] [2] 497664  
97020.cu4 97020cv1 [0, 0, 0, -19992, 1065701] [2] 248832 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 97020.cu have rank \(0\).

Modular form 97020.2.a.cu

sage: E.q_eigenform(10)
 
\( q + q^{5} + q^{11} + 4q^{13} + 4q^{19} + O(q^{20}) \)

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.