Properties

Label 152880.ey
Number of curves 8
Conductor 152880
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("152880.ey1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 152880.ey

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
152880.ey1 152880ca8 [0, 1, 0, -31509316736, -2152824915930060] [2] 127401984  
152880.ey2 152880ca6 [0, 1, 0, -1969333536, -33638337155340] [2, 2] 63700992  
152880.ey3 152880ca7 [0, 1, 0, -1945131456, -34505381511756] [2] 127401984  
152880.ey4 152880ca5 [0, 1, 0, -389181536, -2950404064140] [2] 42467328  
152880.ey5 152880ca3 [0, 1, 0, -124597216, -512038109836] [2] 31850496  
152880.ey6 152880ca2 [0, 1, 0, -32461536, -12600832140] [2, 2] 21233664  
152880.ey7 152880ca1 [0, 1, 0, -20168416, 34668672884] [2] 10616832 \(\Gamma_0(N)\)-optimal
152880.ey8 152880ca4 [0, 1, 0, 127568544, -99849231756] [2] 42467328  

Rank

sage: E.rank()
 

The elliptic curves in class 152880.ey have rank \(2\).

Modular form 152880.2.a.ey

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.