Properties

Label 53550dt
Number of curves $6$
Conductor $53550$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("53550.cs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 53550dt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
53550.cs5 53550dt1 [1, -1, 1, -15804905, -24150226903] [2] 3932160 \(\Gamma_0(N)\)-optimal
53550.cs4 53550dt2 [1, -1, 1, -20412905, -8916178903] [2, 2] 7864320  
53550.cs6 53550dt3 [1, -1, 1, 78731095, -70187170903] [2] 15728640  
53550.cs2 53550dt4 [1, -1, 1, -193284905, 1027278589097] [2, 2] 15728640  
53550.cs3 53550dt5 [1, -1, 1, -65835905, 2361669619097] [2] 31457280  
53550.cs1 53550dt6 [1, -1, 1, -3086685905, 66007278247097] [2] 31457280  

Rank

sage: E.rank()
 

The elliptic curves in class 53550dt have rank \(0\).

Modular form 53550.2.a.cs

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - q^{7} + q^{8} - 4q^{11} + 2q^{13} - q^{14} + q^{16} + q^{17} + 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.