Properties

Label 20592.bl
Number of curves $6$
Conductor $20592$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("20592.bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20592.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20592.bl1 20592bg4 [0, 0, 0, -988419, 378233282] [2] 131072  
20592.bl2 20592bg5 [0, 0, 0, -433299, -106305262] [2] 262144  
20592.bl3 20592bg3 [0, 0, 0, -68259, 4593890] [2, 2] 131072  
20592.bl4 20592bg2 [0, 0, 0, -61779, 5909330] [2, 2] 65536  
20592.bl5 20592bg1 [0, 0, 0, -3459, 112322] [2] 32768 \(\Gamma_0(N)\)-optimal
20592.bl6 20592bg6 [0, 0, 0, 193101, 31304882] [4] 262144  

Rank

sage: E.rank()
 

The elliptic curves in class 20592.bl have rank \(0\).

Modular form 20592.2.a.bl

sage: E.q_eigenform(10)
 
\( q + 2q^{5} - q^{11} + q^{13} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.