Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4560.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4560.e1 4560a4 \([0, -1, 0, -101576, 12494160]\) \(56594125707224978/1262172375\) \(2584929024000\) \([2]\) \(18432\) \(1.4965\)  
4560.e2 4560a3 \([0, -1, 0, -27096, -1525104]\) \(1074299413481138/125244140625\) \(256500000000000\) \([2]\) \(18432\) \(1.4965\)  
4560.e3 4560a2 \([0, -1, 0, -6576, 182160]\) \(30716746229956/4112015625\) \(4210704000000\) \([2, 2]\) \(9216\) \(1.1500\)  
4560.e4 4560a1 \([0, -1, 0, 644, 14656]\) \(115203799856/439833375\) \(-112597344000\) \([2]\) \(4608\) \(0.80338\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4560.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.