Properties

Label 20286.k
Number of curves $6$
Conductor $20286$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("20286.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20286.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20286.k1 20286be5 [1, -1, 0, -34898103, -79341193359] [2] 1572864  
20286.k2 20286be4 [1, -1, 0, -7811883, 8405643861] [2] 786432  
20286.k3 20286be3 [1, -1, 0, -2237643, -1171648395] [2, 2] 786432  
20286.k4 20286be2 [1, -1, 0, -508923, 119705445] [2, 2] 393216  
20286.k5 20286be1 [1, -1, 0, 55557, 10309221] [2] 196608 \(\Gamma_0(N)\)-optimal
20286.k6 20286be6 [1, -1, 0, 2763297, -5669493831] [2] 1572864  

Rank

sage: E.rank()
 

The elliptic curves in class 20286.k have rank \(0\).

Modular form 20286.2.a.k

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.