Properties

Label 271950.bw
Number of curves $6$
Conductor $271950$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("271950.bw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 271950.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
271950.bw1 271950bw4 [1, 1, 0, -417731150, -3286369615500] [2] 63700992  
271950.bw2 271950bw5 [1, 1, 0, -371328150, 2742004687500] [2] 127401984  
271950.bw3 271950bw3 [1, 1, 0, -35923150, -9322527500] [2, 2] 63700992  
271950.bw4 271950bw2 [1, 1, 0, -26123150, -51295927500] [2, 2] 31850496  
271950.bw5 271950bw1 [1, 1, 0, -1035150, -1395895500] [2] 15925248 \(\Gamma_0(N)\)-optimal
271950.bw6 271950bw6 [1, 1, 0, 142681850, -74156142500] [2] 127401984  

Rank

sage: E.rank()
 

The elliptic curves in class 271950.bw have rank \(0\).

Modular form 271950.2.a.bw

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.