Properties

Label 35280dz
Number of curves 4
Conductor 35280
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("35280.bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35280dz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.bk3 35280dz1 [0, 0, 0, -588, -3773] [2] 17280 \(\Gamma_0(N)\)-optimal
35280.bk4 35280dz2 [0, 0, 0, 1617, -25382] [2] 34560  
35280.bk1 35280dz3 [0, 0, 0, -18228, 947023] [2] 51840  
35280.bk2 35280dz4 [0, 0, 0, -16023, 1184722] [2] 103680  

Rank

sage: E.rank()
 

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

Modular form 35280.2.a.bk

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 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.