Properties

Label 62866c
Number of curves 4
Conductor 62866
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("62866.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62866c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62866.d4 62866c1 [1, 1, 0, -5585, -101803] [2] 157248 \(\Gamma_0(N)\)-optimal
62866.d3 62866c2 [1, 1, 0, -79545, -8666371] [2] 314496  
62866.d2 62866c3 [1, 1, 0, -190485, 31915481] [2] 471744  
62866.d1 62866c4 [1, 1, 0, -208975, 25321947] [2] 943488  

Rank

sage: E.rank()
 

The elliptic curves in class 62866c have rank \(0\).

Modular form 62866.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{2} + 2q^{3} + q^{4} - 2q^{6} + 4q^{7} - q^{8} + q^{9} + 6q^{11} + 2q^{12} + 2q^{13} - 4q^{14} + q^{16} - q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.