Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("100800.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800ej

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.f4 100800ej1 [0, 0, 0, 6000, 61000] [2] 221184 \(\Gamma_0(N)\)-optimal
100800.f3 100800ej2 [0, 0, 0, -25500, 502000] [2] 442368  
100800.f2 100800ej3 [0, 0, 0, -102000, 12913000] [2] 663552  
100800.f1 100800ej4 [0, 0, 0, -1645500, 812446000] [2] 1327104  

Rank

sage: E.rank()
 

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

Modular form 100800.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{7} - 6q^{11} + 2q^{13} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.