Properties

Label 100800lv
Number of curves 8
Conductor 100800
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("100800.gt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800lv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.gt7 100800lv1 [0, 0, 0, 3023700, 1524962000] [2] 4718592 \(\Gamma_0(N)\)-optimal
100800.gt6 100800lv2 [0, 0, 0, -15408300, 13653218000] [2, 2] 9437184  
100800.gt5 100800lv3 [0, 0, 0, -108720300, -426592798000] [2, 2] 18874368  
100800.gt4 100800lv4 [0, 0, 0, -217008300, 1230107618000] [2] 18874368  
100800.gt8 100800lv5 [0, 0, 0, 18287700, -1363657822000] [2] 37748736  
100800.gt2 100800lv6 [0, 0, 0, -1728720300, -27665272798000] [2, 2] 37748736  
100800.gt3 100800lv7 [0, 0, 0, -1717920300, -28028001598000] [2] 75497472  
100800.gt1 100800lv8 [0, 0, 0, -27659520300, -1770578063998000] [2] 75497472  

Rank

sage: E.rank()
 

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

Modular form 100800.2.a.gt

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.