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Properties

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

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Show commands: SageMath
E = EllipticCurve("cm1")
 
E.isogeny_class()
 

Elliptic curves in class 206910cm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
206910.dv2 206910cm1 \([1, -1, 1, -67178, -2360663]\) \(961504803/486400\) \(16960590543283200\) \([2]\) \(2073600\) \(1.8067\) \(\Gamma_0(N)\)-optimal
206910.dv1 206910cm2 \([1, -1, 1, -589898, 172855081]\) \(651038076963/7220000\) \(251758765876860000\) \([2]\) \(4147200\) \(2.1533\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 206910.2.a.cm

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.