Properties

Label 338800.w
Number of curves 4
Conductor 338800
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("338800.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 338800.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
338800.w1 338800w4 [0, 1, 0, -1264015408, -16807519120812] [2] 238878720  
338800.w2 338800w2 [0, 1, 0, -173079408, 868584863188] [2] 79626240  
338800.w3 338800w1 [0, 1, 0, -2711408, 33440927188] [2] 39813120 \(\Gamma_0(N)\)-optimal
338800.w4 338800w3 [0, 1, 0, 24392592, -900833952812] [2] 119439360  

Rank

sage: E.rank()
 

The elliptic curves in class 338800.w have rank \(1\).

Modular form 338800.2.a.w

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - q^{7} + q^{9} - 4q^{13} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.