Properties

Label 203280ff
Number of curves $6$
Conductor $203280$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("203280.fx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 203280ff

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.fx4 203280ff1 [0, 1, 0, -21215, 1182300] [2] 327680 \(\Gamma_0(N)\)-optimal
203280.fx3 203280ff2 [0, 1, 0, -21820, 1110668] [2, 2] 655360  
203280.fx5 203280ff3 [0, 1, 0, 29000, 5562500] [2] 1310720  
203280.fx2 203280ff4 [0, 1, 0, -82320, -7915932] [2, 2] 1310720  
203280.fx6 203280ff5 [0, 1, 0, 135480, -42502572] [2] 2621440  
203280.fx1 203280ff6 [0, 1, 0, -1268120, -550063692] [2] 2621440  

Rank

sage: E.rank()
 

The elliptic curves in class 203280ff have rank \(0\).

Modular form 203280.2.a.fx

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} - q^{7} + q^{9} + 2q^{13} + q^{15} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.