Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 570.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
570.d1 570d3 \([1, 0, 1, -1233444, -527363678]\) \(207530301091125281552569/805586668007040\) \(805586668007040\) \([2]\) \(8960\) \(2.0734\)  
570.d2 570d4 \([1, 0, 1, -233764, 33569186]\) \(1412712966892699019449/330160465517040000\) \(330160465517040000\) \([2]\) \(8960\) \(2.0734\)  
570.d3 570d2 \([1, 0, 1, -78244, -7985758]\) \(52974743974734147769/3152005008998400\) \(3152005008998400\) \([2, 2]\) \(4480\) \(1.7268\)  
570.d4 570d1 \([1, 0, 1, 3676, -514654]\) \(5495662324535111/117739817533440\) \(-117739817533440\) \([2]\) \(2240\) \(1.3803\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 570.d do not have complex multiplication.

Modular form 570.2.a.d

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

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.