Properties

Label 5202.c
Number of curves 6
Conductor 5202
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("5202.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5202.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5202.c1 5202b5 [1, -1, 0, -72162198, 235964108794] [2] 294912  
5202.c2 5202b3 [1, -1, 0, -4510188, 3687697660] [2, 2] 147456  
5202.c3 5202b6 [1, -1, 0, -4276098, 4087382926] [2] 294912  
5202.c4 5202b2 [1, -1, 0, -296568, 51343600] [2, 2] 73728  
5202.c5 5202b1 [1, -1, 0, -88488, -9374144] [2] 36864 \(\Gamma_0(N)\)-optimal
5202.c6 5202b4 [1, -1, 0, 587772, 298428196] [2] 147456  

Rank

sage: E.rank()
 

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

Modular form 5202.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - 2q^{5} - q^{8} + 2q^{10} - 4q^{11} - 2q^{13} + q^{16} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.