Properties

Label 206910.eo
Number of curves $4$
Conductor $206910$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("206910.eo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 206910.eo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
206910.eo1 206910q4 [1, -1, 1, -676292, -213586491] [2] 2621440  
206910.eo2 206910q2 [1, -1, 1, -55562, -1048539] [2, 2] 1310720  
206910.eo3 206910q1 [1, -1, 1, -33782, 2383989] [2] 655360 \(\Gamma_0(N)\)-optimal
206910.eo4 206910q3 [1, -1, 1, 216688, -8453739] [2] 2621440  

Rank

sage: E.rank()
 

The elliptic curves in class 206910.eo have rank \(0\).

Modular form 206910.2.a.eo

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.