Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("100800.iy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800.iy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.iy1 100800fr8 [0, 0, 0, -27659520300, 1770578063998000] [2] 75497472  
100800.iy2 100800fr6 [0, 0, 0, -1728720300, 27665272798000] [2, 2] 37748736  
100800.iy3 100800fr7 [0, 0, 0, -1717920300, 28028001598000] [2] 75497472  
100800.iy4 100800fr4 [0, 0, 0, -217008300, -1230107618000] [2] 18874368  
100800.iy5 100800fr3 [0, 0, 0, -108720300, 426592798000] [2, 2] 18874368  
100800.iy6 100800fr2 [0, 0, 0, -15408300, -13653218000] [2, 2] 9437184  
100800.iy7 100800fr1 [0, 0, 0, 3023700, -1524962000] [2] 4718592 \(\Gamma_0(N)\)-optimal
100800.iy8 100800fr5 [0, 0, 0, 18287700, 1363657822000] [2] 37748736  

Rank

sage: E.rank()
 

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

Modular form 100800.2.a.iy

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.