Properties

Label 6171.e
Number of curves 2
Conductor 6171
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6171.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6171.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6171.e1 6171g2 [0, 1, 1, -7179, 231875] [] 8100  
6171.e2 6171g1 [0, 1, 1, 81, 1370] [] 2700 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 6171.e have rank \(0\).

Modular form 6171.2.a.e

sage: E.q_eigenform(10)
 
\( q + q^{3} - 2q^{4} + 3q^{5} + 4q^{7} + q^{9} - 2q^{12} + q^{13} + 3q^{15} + 4q^{16} + q^{17} + q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.