Properties

Label 4560.y
Number of curves $2$
Conductor $4560$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 4560.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.y1 4560i2 \([0, 1, 0, -400, 2948]\) \(6929294404/4275\) \(4377600\) \([2]\) \(1536\) \(0.21684\)  
4560.y2 4560i1 \([0, 1, 0, -20, 60]\) \(-3631696/5415\) \(-1386240\) \([2]\) \(768\) \(-0.12974\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4560.2.a.y

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