Properties

Label 5520.d
Number of curves $2$
Conductor $5520$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 5520.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.d1 5520l2 \([0, -1, 0, -12576, 380160]\) \(53706380371489/16171875000\) \(66240000000000\) \([2]\) \(11520\) \(1.3573\)  
5520.d2 5520l1 \([0, -1, 0, 2144, 38656]\) \(265971760991/317400000\) \(-1300070400000\) \([2]\) \(5760\) \(1.0107\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5520.2.a.d

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