Properties

Label 560.b
Number of curves $3$
Conductor $560$
CM no
Rank $0$
Graph

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

Elliptic curves in class 560.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
560.b1 560c3 \([0, -1, 0, -2101, 39485]\) \(-250523582464/13671875\) \(-56000000000\) \([]\) \(432\) \(0.82061\)  
560.b2 560c1 \([0, -1, 0, -21, -35]\) \(-262144/35\) \(-143360\) \([]\) \(48\) \(-0.27800\) \(\Gamma_0(N)\)-optimal
560.b3 560c2 \([0, -1, 0, 139, 61]\) \(71991296/42875\) \(-175616000\) \([]\) \(144\) \(0.27130\)  

Rank

sage: E.rank()
 

The elliptic curves in class 560.b have rank \(0\).

Complex multiplication

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

Modular form 560.2.a.b

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - q^{7} - 2q^{9} + 3q^{11} + 5q^{13} + q^{15} + 3q^{17} - 2q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.