Properties

Label 100800lw
Number of curves $6$
Conductor $100800$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("100800.gr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800lw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.gr4 100800lw1 [0, 0, 0, -157800, 24127000] [2] 393216 \(\Gamma_0(N)\)-optimal
100800.gr3 100800lw2 [0, 0, 0, -162300, 22678000] [2, 2] 786432  
100800.gr5 100800lw3 [0, 0, 0, 215700, 112642000] [2] 1572864  
100800.gr2 100800lw4 [0, 0, 0, -612300, -160022000] [2, 2] 1572864  
100800.gr6 100800lw5 [0, 0, 0, 1007700, -863102000] [2] 3145728  
100800.gr1 100800lw6 [0, 0, 0, -9432300, -11149742000] [2] 3145728  

Rank

sage: E.rank()
 

The elliptic curves in class 100800lw have rank \(1\).

Modular form 100800.2.a.gr

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.