Properties

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

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

Elliptic curves in class 206910.eo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
206910.eo1 206910q4 \([1, -1, 1, -676292, -213586491]\) \(26487576322129/44531250\) \(57510682994531250\) \([2]\) \(2621440\) \(2.1112\)  
206910.eo2 206910q2 \([1, -1, 1, -55562, -1048539]\) \(14688124849/8122500\) \(10489948578202500\) \([2, 2]\) \(1310720\) \(1.7646\)  
206910.eo3 206910q1 \([1, -1, 1, -33782, 2383989]\) \(3301293169/22800\) \(29445469693200\) \([2]\) \(655360\) \(1.4180\) \(\Gamma_0(N)\)-optimal
206910.eo4 206910q3 \([1, -1, 1, 216688, -8453739]\) \(871257511151/527800050\) \(-681636858611598450\) \([2]\) \(2621440\) \(2.1112\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 206910.eo do not have complex multiplication.

Modular form 206910.2.a.eo

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

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.