Properties

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

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

Elliptic curves in class 328560.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
328560.bx1 328560bx4 \([0, 1, 0, -7469373976, -248472751706476]\) \(4385367890843575421521/24975000000\) \(262467653897318400000000\) \([2]\) \(226934784\) \(4.1054\)  
328560.bx2 328560bx5 \([0, 1, 0, -6639650456, 207333307020180]\) \(3080272010107543650001/15465841417699560\) \(162533858356419629546209443840\) \([2]\) \(453869568\) \(4.4520\)  
328560.bx3 328560bx3 \([0, 1, 0, -642335256, -703961563500]\) \(2788936974993502801/1593609593601600\) \(16747586436871710902904422400\) \([2, 2]\) \(226934784\) \(4.1054\)  
328560.bx4 328560bx2 \([0, 1, 0, -467103256, -3877833640300]\) \(1072487167529950801/2554882560000\) \(26849811071326318755840000\) \([2, 2]\) \(113467392\) \(3.7589\)  
328560.bx5 328560bx1 \([0, 1, 0, -18509336, -105517648236]\) \(-66730743078481/419010969600\) \(-4403476522448552617574400\) \([2]\) \(56733696\) \(3.4123\) \(\Gamma_0(N)\)-optimal
328560.bx6 328560bx6 \([0, 1, 0, 2551267944, -5610613519980]\) \(174751791402194852399/102423900876336360\) \(-1076394833474414354509542359040\) \([2]\) \(453869568\) \(4.4520\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 328560.bx do not have complex multiplication.

Modular form 328560.2.a.bx

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

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.