Properties

Label 35280.ek
Number of curves 8
Conductor 35280
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("35280.ek1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 35280.ek

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.ek1 35280fe8 [0, 0, 0, -2478296667, 47487362908426] [4] 10616832  
35280.ek2 35280fe6 [0, 0, 0, -154896987, 741955386634] [2, 2] 5308416  
35280.ek3 35280fe7 [0, 0, 0, -143607387, 854695590154] [2] 10616832  
35280.ek4 35280fe5 [0, 0, 0, -30746667, 64467598426] [4] 3538944  
35280.ek5 35280fe3 [0, 0, 0, -10390107, 9796828426] [2] 2654208  
35280.ek6 35280fe2 [0, 0, 0, -4074987, -1662164966] [2, 2] 1769472  
35280.ek7 35280fe1 [0, 0, 0, -3510507, -2530673894] [2] 884736 \(\Gamma_0(N)\)-optimal
35280.ek8 35280fe4 [0, 0, 0, 13565013, -12207356966] [2] 3538944  

Rank

sage: E.rank()
 

The elliptic curves in class 35280.ek have rank \(1\).

Modular form 35280.2.a.ek

sage: E.q_eigenform(10)
 
\( q + q^{5} - 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.