Properties

Label 35280.bj
Number of curves $8$
Conductor $35280$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("35280.bj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35280.bj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.bj1 35280dy8 [0, 0, 0, -45518403, -74365731902] [2] 5308416  
35280.bj2 35280dy5 [0, 0, 0, -40649763, -99755096798] [2] 1769472  
35280.bj3 35280dy6 [0, 0, 0, -19058403, 31172624098] [2, 2] 2654208  
35280.bj4 35280dy3 [0, 0, 0, -18917283, 31669112482] [2] 1327104  
35280.bj5 35280dy2 [0, 0, 0, -2547363, -1549971038] [2, 2] 884736  
35280.bj6 35280dy4 [0, 0, 0, -571683, -3892732382] [2] 1769472  
35280.bj7 35280dy1 [0, 0, 0, -289443, 21089698] [2] 442368 \(\Gamma_0(N)\)-optimal
35280.bj8 35280dy7 [0, 0, 0, 5143677, 104935723522] [2] 5308416  

Rank

sage: E.rank()
 

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

Modular form 35280.2.a.bj

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.