Properties

Label 4560.j
Number of curves $4$
Conductor $4560$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.j1 4560f3 \([0, -1, 0, -480, -3600]\) \(11968836484/961875\) \(984960000\) \([2]\) \(2048\) \(0.46886\)  
4560.j2 4560f2 \([0, -1, 0, -100, 352]\) \(436334416/81225\) \(20793600\) \([2, 2]\) \(1024\) \(0.12229\)  
4560.j3 4560f1 \([0, -1, 0, -95, 390]\) \(5988775936/285\) \(4560\) \([2]\) \(512\) \(-0.22429\) \(\Gamma_0(N)\)-optimal
4560.j4 4560f4 \([0, -1, 0, 200, 1792]\) \(859687196/1954815\) \(-2001730560\) \([4]\) \(2048\) \(0.46886\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4560.2.a.j

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.