Properties

Label 35280.el
Number of curves $4$
Conductor $35280$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("35280.el1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35280.el

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.el1 35280dg3 [0, 0, 0, -329427, -63771246] [2] 331776  
35280.el2 35280dg1 [0, 0, 0, -82467, 9103906] [2] 110592 \(\Gamma_0(N)\)-optimal
35280.el3 35280dg2 [0, 0, 0, -58947, 14405314] [2] 221184  
35280.el4 35280dg4 [0, 0, 0, 517293, -337600494] [2] 663552  

Rank

sage: E.rank()
 

The elliptic curves in class 35280.el have rank \(0\).

Modular form 35280.2.a.el

sage: E.q_eigenform(10)
 
\( q + q^{5} - 2q^{13} + 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.