Properties

Label 206310.bi
Number of curves $6$
Conductor $206310$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("206310.bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 206310.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
206310.bi1 206310bg5 [1, 1, 1, -4768946, 4006510949] [2] 5767168  
206310.bi2 206310bg4 [1, 1, 1, -447016, -115131187] [2] 2883584  
206310.bi3 206310bg3 [1, 1, 1, -298896, 62138829] [2, 2] 2883584  
206310.bi4 206310bg6 [1, 1, 1, -60846, 158691909] [2] 5767168  
206310.bi5 206310bg2 [1, 1, 1, -34396, -917971] [2, 2] 1441792  
206310.bi6 206310bg1 [1, 1, 1, 7924, -105427] [2] 720896 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 206310.bi have rank \(0\).

Modular form 206310.2.a.bi

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + q^{8} + q^{9} - q^{10} - 4q^{11} - q^{12} + q^{13} + q^{15} + q^{16} + 6q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.