Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("35280.fr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35280ck

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.fr3 35280ck1 [0, 0, 0, -882, -9261] [2] 18432 \(\Gamma_0(N)\)-optimal
35280.fr2 35280ck2 [0, 0, 0, -3087, 55566] [2, 2] 36864  
35280.fr4 35280ck3 [0, 0, 0, 5733, 314874] [2] 73728  
35280.fr1 35280ck4 [0, 0, 0, -47187, 3945186] [2] 73728  

Rank

sage: E.rank()
 

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

Modular form 35280.2.a.fr

sage: E.q_eigenform(10)
 
\( q + q^{5} + 4q^{11} + 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.