Properties

Label 570.k
Number of curves $4$
Conductor $570$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("570.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 570.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
570.k1 570k4 [1, 0, 0, -463231, 77449961] [2] 17280  
570.k2 570k2 [1, 0, 0, -414991, 102863225] [6] 5760  
570.k3 570k1 [1, 0, 0, -25871, 1614201] [6] 2880 \(\Gamma_0(N)\)-optimal
570.k4 570k3 [1, 0, 0, 85489, 8420985] [2] 8640  

Rank

sage: E.rank()
 

The elliptic curves in class 570.k have rank \(0\).

Modular form 570.2.a.k

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} + q^{8} + q^{9} - q^{10} + 6q^{11} + q^{12} - 4q^{13} + 2q^{14} - q^{15} + q^{16} - 6q^{17} + q^{18} + q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.