Properties

Label 560.d
Number of curves $4$
Conductor $560$
CM no
Rank $1$
Graph

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

Elliptic curves in class 560.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
560.d1 560d4 \([0, 0, 0, -4283, 107882]\) \(2121328796049/120050\) \(491724800\) \([4]\) \(384\) \(0.73213\)  
560.d2 560d3 \([0, 0, 0, -1403, -18902]\) \(74565301329/5468750\) \(22400000000\) \([2]\) \(384\) \(0.73213\)  
560.d3 560d2 \([0, 0, 0, -283, 1482]\) \(611960049/122500\) \(501760000\) \([2, 2]\) \(192\) \(0.38556\)  
560.d4 560d1 \([0, 0, 0, 37, 138]\) \(1367631/2800\) \(-11468800\) \([2]\) \(96\) \(0.038988\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 560.d have rank \(1\).

Complex multiplication

The elliptic curves in class 560.d do not have complex multiplication.

Modular form 560.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{5} + q^{7} - 3q^{9} - 4q^{11} - 6q^{13} + 2q^{17} + O(q^{20})\)  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.