Properties

Label 286650j
Number of curves 4
Conductor 286650
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("286650.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 286650j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
286650.j3 286650j1 [1, -1, 0, -8362692, -4177561284] [2] 31850496 \(\Gamma_0(N)\)-optimal
286650.j4 286650j2 [1, -1, 0, 29453058, -31518348534] [2] 63700992  
286650.j1 286650j3 [1, -1, 0, -567495567, -5203311064659] [2] 95551488  
286650.j2 286650j4 [1, -1, 0, -564408567, -5262720379659] [2] 191102976  

Rank

sage: E.rank()
 

The elliptic curves in class 286650j have rank \(0\).

Modular form 286650.2.a.j

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{8} - 6q^{11} + q^{13} + q^{16} - 8q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.