Properties

Label 203280.ee
Number of curves $4$
Conductor $203280$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("ee1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 203280.ee

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
203280.ee1 203280fv3 \([0, 1, 0, -3602936, 2630652660]\) \(1425631925916578/270703125\) \(982153418400000000\) \([2]\) \(3932160\) \(2.4535\)  
203280.ee2 203280fv4 \([0, 1, 0, -1579816, -740631916]\) \(120186986927618/4332064275\) \(15717409011882547200\) \([2]\) \(3932160\) \(2.4535\)  
203280.ee3 203280fv2 \([0, 1, 0, -248816, 31880484]\) \(939083699236/300155625\) \(544505855160960000\) \([2, 2]\) \(1966080\) \(2.1069\)  
203280.ee4 203280fv1 \([0, 1, 0, 44004, 3418380]\) \(20777545136/23059575\) \(-10457969599123200\) \([2]\) \(983040\) \(1.7603\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 203280.2.a.ee

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.