Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("100800.mj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800mw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.mj7 100800mw1 [0, 0, 0, -7164300, 7378058000] [2] 3538944 \(\Gamma_0(N)\)-optimal
100800.mj6 100800mw2 [0, 0, 0, -8316300, 4845962000] [2, 2] 7077888  
100800.mj5 100800mw3 [0, 0, 0, -21204300, -28562182000] [2] 10616832  
100800.mj8 100800mw4 [0, 0, 0, 27683700, 35589962000] [2] 14155776  
100800.mj4 100800mw5 [0, 0, 0, -62748300, -187952182000] [2] 14155776  
100800.mj2 100800mw6 [0, 0, 0, -316116300, -2163135238000] [2, 2] 21233664  
100800.mj3 100800mw7 [0, 0, 0, -293076300, -2491823878000] [2] 42467328  
100800.mj1 100800mw8 [0, 0, 0, -5057748300, -138447122182000] [2] 42467328  

Rank

sage: E.rank()
 

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

Modular form 100800.2.a.mj

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.