Properties

Label 570.b
Number of curves $2$
Conductor $570$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 570.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
570.b1 570a2 \([1, 1, 0, -1618, 24388]\) \(468898230633769/5540400\) \(5540400\) \([2]\) \(384\) \(0.44399\)  
570.b2 570a1 \([1, 1, 0, -98, 372]\) \(-105756712489/12476160\) \(-12476160\) \([2]\) \(192\) \(0.097417\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 570.b have rank \(1\).

Complex multiplication

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

Modular form 570.2.a.b

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.