Properties

Label 5202.d
Number of curves 4
Conductor 5202
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("5202.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5202.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5202.d1 5202a4 [1, -1, 0, -293967, 42466387] [2] 82944  
5202.d2 5202a3 [1, -1, 0, -267957, 53447809] [2] 41472  
5202.d3 5202a2 [1, -1, 0, -111897, -14375867] [2] 27648  
5202.d4 5202a1 [1, -1, 0, -7857, -164003] [2] 13824 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5202.d have rank \(0\).

Modular form 5202.2.a.d

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + 4q^{7} - q^{8} + 6q^{11} + 2q^{13} - 4q^{14} + q^{16} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.