Properties

Label 4560.n
Number of curves $6$
Conductor $4560$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.n1 4560d5 \([0, -1, 0, -693120, 222337440]\) \(17981241677724245762/16245\) \(33269760\) \([4]\) \(16384\) \(1.6386\)  
4560.n2 4560d4 \([0, -1, 0, -43320, 3484800]\) \(8780093172522724/263900025\) \(270233625600\) \([2, 4]\) \(8192\) \(1.2920\)  
4560.n3 4560d6 \([0, -1, 0, -41520, 3785760]\) \(-3865238121540962/764260336845\) \(-1565205169858560\) \([4]\) \(16384\) \(1.6386\)  
4560.n4 4560d3 \([0, -1, 0, -12320, -474000]\) \(201971983086724/20447192475\) \(20937925094400\) \([2]\) \(8192\) \(1.2920\)  
4560.n5 4560d2 \([0, -1, 0, -2820, 50400]\) \(9691367618896/1480325625\) \(378963360000\) \([2, 2]\) \(4096\) \(0.94545\)  
4560.n6 4560d1 \([0, -1, 0, 305, 4150]\) \(195469297664/601171875\) \(-9618750000\) \([2]\) \(2048\) \(0.59887\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4560.n have rank \(1\).

Complex multiplication

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

Modular form 4560.2.a.n

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.