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("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 570.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
570.l1 570l4 \([1, 0, 0, -52823445, -147775056075]\) \(16300610738133468173382620881/2228489100\) \(2228489100\) \([2]\) \(24000\) \(2.6088\)  
570.l2 570l3 \([1, 0, 0, -3301465, -2309192023]\) \(-3979640234041473454886161/1471455901872240\) \(-1471455901872240\) \([2]\) \(12000\) \(2.2623\)  
570.l3 570l2 \([1, 0, 0, -87945, -8655975]\) \(75224183150104868881/11219310000000000\) \(11219310000000000\) \([10]\) \(4800\) \(1.8041\)  
570.l4 570l1 \([1, 0, 0, 9335, -737383]\) \(89962967236397039/287450726400000\) \(-287450726400000\) \([10]\) \(2400\) \(1.4575\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 570.2.a.l

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.