Properties

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

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

Elliptic curves in class 5202.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5202.d1 5202a4 \([1, -1, 0, -293967, 42466387]\) \(159661140625/48275138\) \(849463221880991538\) \([2]\) \(82944\) \(2.1454\)  
5202.d2 5202a3 \([1, -1, 0, -267957, 53447809]\) \(120920208625/19652\) \(345802247865252\) \([2]\) \(41472\) \(1.7988\)  
5202.d3 5202a2 \([1, -1, 0, -111897, -14375867]\) \(8805624625/2312\) \(40682617395912\) \([2]\) \(27648\) \(1.5961\)  
5202.d4 5202a1 \([1, -1, 0, -7857, -164003]\) \(3048625/1088\) \(19144761127488\) \([2]\) \(13824\) \(1.2495\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 5202.d do not have complex multiplication.

Modular form 5202.2.a.d

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.