Properties

Label 328560.bx
Number of curves $6$
Conductor $328560$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("328560.bx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 328560.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
328560.bx1 328560bx4 [0, 1, 0, -7469373976, -248472751706476] [2] 226934784  
328560.bx2 328560bx5 [0, 1, 0, -6639650456, 207333307020180] [2] 453869568  
328560.bx3 328560bx3 [0, 1, 0, -642335256, -703961563500] [2, 2] 226934784  
328560.bx4 328560bx2 [0, 1, 0, -467103256, -3877833640300] [2, 2] 113467392  
328560.bx5 328560bx1 [0, 1, 0, -18509336, -105517648236] [2] 56733696 \(\Gamma_0(N)\)-optimal
328560.bx6 328560bx6 [0, 1, 0, 2551267944, -5610613519980] [2] 453869568  

Rank

sage: E.rank()
 

The elliptic curves in class 328560.bx have rank \(1\).

Modular form 328560.2.a.bx

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} + q^{9} - 4q^{11} + 2q^{13} - q^{15} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.