Properties

Label 570.j
Number of curves $2$
Conductor $570$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("570.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 570.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
570.j1 570j2 [1, 0, 0, -23326, -1373170] [2] 1120  
570.j2 570j1 [1, 0, 0, -1456, -21604] [2] 560 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 570.2.a.j

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

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.