Properties

Label 100800ed
Number of curves 4
Conductor 100800
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("100800.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.w4 100800ed1 [0, 0, 0, -661575, 862373500] [2] 2949120 \(\Gamma_0(N)\)-optimal
100800.w3 100800ed2 [0, 0, 0, -18239700, 29901436000] [2, 2] 5898240  
100800.w2 100800ed3 [0, 0, 0, -26114700, 1567186000] [2] 11796480  
100800.w1 100800ed4 [0, 0, 0, -291614700, 1916735686000] [2] 11796480  

Rank

sage: E.rank()
 

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

Modular form 100800.2.a.w

sage: E.q_eigenform(10)
 
\( q - q^{7} - 4q^{11} - 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.