Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.s1 4560x3 \([0, 1, 0, -9936, 377364]\) \(26487576322129/44531250\) \(182400000000\) \([2]\) \(6144\) \(1.0561\)  
4560.s2 4560x2 \([0, 1, 0, -816, 1620]\) \(14688124849/8122500\) \(33269760000\) \([2, 2]\) \(3072\) \(0.70949\)  
4560.s3 4560x1 \([0, 1, 0, -496, -4396]\) \(3301293169/22800\) \(93388800\) \([2]\) \(1536\) \(0.36292\) \(\Gamma_0(N)\)-optimal
4560.s4 4560x4 \([0, 1, 0, 3184, 16020]\) \(871257511151/527800050\) \(-2161869004800\) \([4]\) \(6144\) \(1.0561\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4560.2.a.s

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