Properties

Label 100800.ea
Number of curves 8
Conductor 100800
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("100800.ea1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800.ea

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.ea1 100800cy8 [0, 0, 0, -5057748300, 138447122182000] [2] 42467328  
100800.ea2 100800cy6 [0, 0, 0, -316116300, 2163135238000] [2, 2] 21233664  
100800.ea3 100800cy7 [0, 0, 0, -293076300, 2491823878000] [2] 42467328  
100800.ea4 100800cy5 [0, 0, 0, -62748300, 187952182000] [2] 14155776  
100800.ea5 100800cy3 [0, 0, 0, -21204300, 28562182000] [2] 10616832  
100800.ea6 100800cy2 [0, 0, 0, -8316300, -4845962000] [2, 2] 7077888  
100800.ea7 100800cy1 [0, 0, 0, -7164300, -7378058000] [2] 3538944 \(\Gamma_0(N)\)-optimal
100800.ea8 100800cy4 [0, 0, 0, 27683700, -35589962000] [2] 14155776  

Rank

sage: E.rank()
 

The elliptic curves in class 100800.ea have rank \(0\).

Modular form 100800.2.a.ea

sage: E.q_eigenform(10)
 
\( q - q^{7} + 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20}) \)

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.