Properties

Label 2520.j
Number of curves $4$
Conductor $2520$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 2520.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2520.j1 2520r3 \([0, 0, 0, -15627, -707866]\) \(282678688658/18600435\) \(27770300651520\) \([2]\) \(6144\) \(1.3292\)  
2520.j2 2520r2 \([0, 0, 0, -3027, 50654]\) \(4108974916/893025\) \(666639590400\) \([2, 2]\) \(3072\) \(0.98263\)  
2520.j3 2520r1 \([0, 0, 0, -2847, 58466]\) \(13674725584/945\) \(176359680\) \([4]\) \(1536\) \(0.63606\) \(\Gamma_0(N)\)-optimal
2520.j4 2520r4 \([0, 0, 0, 6693, 309206]\) \(22208984782/40516875\) \(-60491370240000\) \([2]\) \(6144\) \(1.3292\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2520.j have rank \(0\).

Complex multiplication

The elliptic curves in class 2520.j do not have complex multiplication.

Modular form 2520.2.a.j

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.