Properties

Label 203280dj
Number of curves $4$
Conductor $203280$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 203280dj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
203280.bp3 203280dj1 \([0, -1, 0, -322021, 71484976]\) \(-130287139815424/2250652635\) \(-63794694923411760\) \([2]\) \(2488320\) \(2.0225\) \(\Gamma_0(N)\)-optimal
203280.bp2 203280dj2 \([0, -1, 0, -5173516, 4530979180]\) \(33766427105425744/9823275\) \(4455047905862400\) \([2]\) \(4976640\) \(2.3691\)  
203280.bp4 203280dj3 \([0, -1, 0, 1246139, 341639740]\) \(7549996227362816/6152409907875\) \(-174389911180879086000\) \([2]\) \(7464960\) \(2.5718\)  
203280.bp1 203280dj4 \([0, -1, 0, -6001156, 2985452956]\) \(52702650535889104/22020583921875\) \(9986766764344524000000\) \([2]\) \(14929920\) \(2.9184\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 203280.2.a.dj

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} + q^{7} + q^{9} - 2q^{13} + q^{15} + 6q^{17} + 8q^{19} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.