Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("dk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 203280.dk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
203280.dk1 203280cm6 [0, -1, 0, -5903251240, -174574223474000] [2] 58982400  
203280.dk2 203280cm4 [0, -1, 0, -368953240, -2727629416400] [2, 2] 29491200  
203280.dk3 203280cm5 [0, -1, 0, -367123720, -2756020639568] [2] 58982400  
203280.dk4 203280cm3 [0, -1, 0, -49261560, 70195294512] [2] 29491200  
203280.dk5 203280cm2 [0, -1, 0, -23173960, -42169216208] [2, 2] 14745600  
203280.dk6 203280cm1 [0, -1, 0, 67720, -1970406480] [2] 7372800 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 203280.dk do not have complex multiplication.

Modular form 203280.2.a.dk

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.