Properties

Label 4560.b
Number of curves $4$
Conductor $4560$
CM no
Rank $0$
Graph

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

Elliptic curves in class 4560.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.b1 4560n4 \([0, -1, 0, -7411696, -4956797504]\) \(10993009831928446009969/3767761230468750000\) \(15432750000000000000000\) \([2]\) \(414720\) \(2.9595\)  
4560.b2 4560n2 \([0, -1, 0, -6639856, -6583246400]\) \(7903870428425797297009/886464000000\) \(3630956544000000\) \([2]\) \(138240\) \(2.4102\)  
4560.b3 4560n1 \([0, -1, 0, -413936, -103308864]\) \(-1914980734749238129/20440940544000\) \(-83726092468224000\) \([2]\) \(69120\) \(2.0636\) \(\Gamma_0(N)\)-optimal
4560.b4 4560n3 \([0, -1, 0, 1367824, -538943040]\) \(69096190760262356111/70568821500000000\) \(-289049892864000000000\) \([2]\) \(207360\) \(2.6129\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4560.b have rank \(0\).

Complex multiplication

The elliptic curves in class 4560.b do not have complex multiplication.

Modular form 4560.2.a.b

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

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.