Properties

Label 203280x
Number of curves $6$
Conductor $203280$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("203280.gb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 203280x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.gb4 203280x1 [0, 1, 0, -513080, 141285780] [2] 1966080 \(\Gamma_0(N)\)-optimal
203280.gb3 203280x2 [0, 1, 0, -522760, 135667508] [2, 2] 3932160  
203280.gb5 203280x3 [0, 1, 0, 493640, 600365588] [2] 7864320  
203280.gb2 203280x4 [0, 1, 0, -1694040, -688445100] [2, 2] 7864320  
203280.gb6 203280x5 [0, 1, 0, 3523480, -4088181132] [4] 15728640  
203280.gb1 203280x6 [0, 1, 0, -25652040, -50013175500] [2] 15728640  

Rank

sage: E.rank()
 

The elliptic curves in class 203280x have rank \(1\).

Modular form 203280.2.a.gb

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} - q^{7} + q^{9} + 2q^{13} + q^{15} + 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.