Properties

Label 364560ek
Number of curves $6$
Conductor $364560$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("364560.ek1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 364560ek

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
364560.ek6 364560ek1 [0, 1, 0, 47024, -22221676] [2] 4718592 \(\Gamma_0(N)\)-optimal
364560.ek5 364560ek2 [0, 1, 0, -956496, -340538220] [2, 2] 9437184  
364560.ek4 364560ek3 [0, 1, 0, -2900816, 1481678484] [2] 18874368  
364560.ek2 364560ek4 [0, 1, 0, -15068496, -22518957420] [2, 2] 18874368  
364560.ek3 364560ek5 [0, 1, 0, -14833296, -23255697900] [2] 37748736  
364560.ek1 364560ek6 [0, 1, 0, -241095696, -1440975253740] [2] 37748736  

Rank

sage: E.rank()
 

The elliptic curves in class 364560ek have rank \(0\).

Modular form 364560.2.a.ek

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} + q^{9} + 4q^{11} - 6q^{13} - q^{15} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.