Properties

Label 5520.e
Number of curves $4$
Conductor $5520$
CM no
Rank $0$
Graph

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

Elliptic curves in class 5520.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.e1 5520a4 \([0, -1, 0, -2160176, 1222750176]\) \(544328872410114151778/14166950625\) \(29013914880000\) \([4]\) \(49152\) \(2.0986\)  
5520.e2 5520a3 \([0, -1, 0, -209696, -4219680]\) \(497927680189263938/284271240234375\) \(582187500000000000\) \([2]\) \(49152\) \(2.0986\)  
5520.e3 5520a2 \([0, -1, 0, -135176, 19090176]\) \(266763091319403556/1355769140625\) \(1388307600000000\) \([2, 2]\) \(24576\) \(1.7520\)  
5520.e4 5520a1 \([0, -1, 0, -3956, 614400]\) \(-26752376766544/618796614375\) \(-158411933280000\) \([2]\) \(12288\) \(1.4054\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5520.e have rank \(0\).

Complex multiplication

The elliptic curves in class 5520.e do not have complex multiplication.

Modular form 5520.2.a.e

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.