Properties

Label 62866e
Number of curves $2$
Conductor $62866$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("62866.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 62866e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
62866.e2 62866e1 [1, -1, 1, -203737, 36268857] [] 455112 \(\Gamma_0(N)\)-optimal
62866.e1 62866e2 [1, -1, 1, -2588947, -4976806507] [] 3185784  

Rank

sage: E.rank()
 

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

Modular form 62866.2.a.e

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{5} - 3q^{7} + q^{8} - 3q^{9} + q^{10} - 2q^{11} + 2q^{13} - 3q^{14} + q^{16} - q^{17} - 3q^{18} + q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.