Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.q1 4560t4 \([0, -1, 0, -15480, 746352]\) \(100162392144121/23457780\) \(96083066880\) \([4]\) \(12288\) \(1.0978\)  
4560.q2 4560t3 \([0, -1, 0, -7160, -224400]\) \(9912050027641/311647500\) \(1276508160000\) \([2]\) \(12288\) \(1.0978\)  
4560.q3 4560t2 \([0, -1, 0, -1080, 9072]\) \(34043726521/11696400\) \(47908454400\) \([2, 2]\) \(6144\) \(0.75126\)  
4560.q4 4560t1 \([0, -1, 0, 200, 880]\) \(214921799/218880\) \(-896532480\) \([2]\) \(3072\) \(0.40469\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4560.2.a.q

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.