Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("570.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 570.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
570.l1 570l4 [1, 0, 0, -52823445, -147775056075] [2] 24000  
570.l2 570l3 [1, 0, 0, -3301465, -2309192023] [2] 12000  
570.l3 570l2 [1, 0, 0, -87945, -8655975] [10] 4800  
570.l4 570l1 [1, 0, 0, 9335, -737383] [10] 2400 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 570.2.a.l

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.