Properties

Label 206910fa
Number of curves $2$
Conductor $206910$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("fa1")
 
E.isogeny_class()
 

Elliptic curves in class 206910fa

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
206910.cr2 206910fa1 \([1, -1, 0, -7464, 89920]\) \(961504803/486400\) \(23265556300800\) \([2]\) \(691200\) \(1.2574\) \(\Gamma_0(N)\)-optimal
206910.cr1 206910fa2 \([1, -1, 0, -65544, -6380192]\) \(651038076963/7220000\) \(345348101340000\) \([2]\) \(1382400\) \(1.6040\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 206910.2.a.fa

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + q^{5} + 4 q^{7} - q^{8} - q^{10} - 4 q^{14} + q^{16} - 4 q^{17} + q^{19} + O(q^{20})\) Copy content 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.