Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("100800.ja1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800.ja

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.ja1 100800fq6 [0, 0, 0, -9432300, 11149742000] [2] 3145728  
100800.ja2 100800fq4 [0, 0, 0, -612300, 160022000] [2, 2] 1572864  
100800.ja3 100800fq2 [0, 0, 0, -162300, -22678000] [2, 2] 786432  
100800.ja4 100800fq1 [0, 0, 0, -157800, -24127000] [2] 393216 \(\Gamma_0(N)\)-optimal
100800.ja5 100800fq3 [0, 0, 0, 215700, -112642000] [2] 1572864  
100800.ja6 100800fq5 [0, 0, 0, 1007700, 863102000] [2] 3145728  

Rank

sage: E.rank()
 

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

Modular form 100800.2.a.ja

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.