Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("100800.jq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800fu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.jq5 100800fu1 [0, 0, 0, -57900, -11842000] [2] 786432 \(\Gamma_0(N)\)-optimal
100800.jq4 100800fu2 [0, 0, 0, -1209900, -511810000] [2, 2] 1572864  
100800.jq3 100800fu3 [0, 0, 0, -1497900, -249730000] [2, 2] 3145728  
100800.jq1 100800fu4 [0, 0, 0, -19353900, -32771842000] [2] 3145728  
100800.jq6 100800fu5 [0, 0, 0, 5558100, -1929058000] [2] 6291456  
100800.jq2 100800fu6 [0, 0, 0, -13161900, 18202718000] [2] 6291456  

Rank

sage: E.rank()
 

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

Modular form 100800.2.a.jq

sage: E.q_eigenform(10)
 
\( q + q^{7} - 4q^{11} + 6q^{13} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.