Properties

Label 202800fw
Number of curves $6$
Conductor $202800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("202800.dm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 202800fw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
202800.dm6 202800fw1 [0, -1, 0, 1012592, -157402688] [2] 6193152 \(\Gamma_0(N)\)-optimal
202800.dm5 202800fw2 [0, -1, 0, -4395408, -1303898688] [2, 2] 12386304  
202800.dm3 202800fw3 [0, -1, 0, -38195408, 89956101312] [2, 2] 24772608  
202800.dm2 202800fw4 [0, -1, 0, -57123408, -166026170688] [2] 24772608  
202800.dm1 202800fw5 [0, -1, 0, -609415408, 5790731701312] [2] 49545216  
202800.dm4 202800fw6 [0, -1, 0, -7775408, 229279701312] [2] 49545216  

Rank

sage: E.rank()
 

The elliptic curves in class 202800fw have rank \(0\).

Modular form 202800.2.a.dm

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{9} + 4q^{11} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.