Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("570.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 570.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
570.i1 570i4 [1, 1, 1, -492480, 132819117] [2] 3840  
570.i2 570i3 [1, 1, 1, -31160, 2011565] [2] 3840  
570.i3 570i2 [1, 1, 1, -30780, 2065677] [2, 2] 1920  
570.i4 570i1 [1, 1, 1, -1900, 32525] [4] 960 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 570.2.a.i

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.