Properties

Label 4560.v
Number of curves $2$
Conductor $4560$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.v1 4560y2 \([0, 1, 0, -1496, 21204]\) \(90458382169/2671875\) \(10944000000\) \([2]\) \(3072\) \(0.70349\)  
4560.v2 4560y1 \([0, 1, 0, 24, 1140]\) \(357911/135375\) \(-554496000\) \([2]\) \(1536\) \(0.35691\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4560.2.a.v

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.