Properties

Label 277970.bb
Number of curves 4
Conductor 277970
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("277970.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 277970.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
277970.bb1 277970bb4 [1, 1, 0, -9427883, 10822507073] [2] 23887872  
277970.bb2 277970bb2 [1, 1, 0, -1290943, -560081403] [2] 7962624  
277970.bb3 277970bb1 [1, 1, 0, -20223, -21550267] [2] 3981312 \(\Gamma_0(N)\)-optimal
277970.bb4 277970bb3 [1, 1, 0, 181937, 580360917] [2] 11943936  

Rank

sage: E.rank()
 

The elliptic curves in class 277970.bb have rank \(1\).

Modular form 277970.2.a.bb

sage: E.q_eigenform(10)
 
\( q - q^{2} + 2q^{3} + q^{4} - q^{5} - 2q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - q^{11} + 2q^{12} + 4q^{13} - q^{14} - 2q^{15} + q^{16} - q^{18} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.