Properties

Label 840.j
Number of curves 6
Conductor 840
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("840.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 840.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
840.j1 840j4 [0, 1, 0, -6720, 209808] [4] 512  
840.j2 840j5 [0, 1, 0, -6480, -202272] [2] 1024  
840.j3 840j3 [0, 1, 0, -600, 0] [2, 2] 512  
840.j4 840j2 [0, 1, 0, -420, 3168] [2, 4] 256  
840.j5 840j1 [0, 1, 0, -15, 90] [4] 128 \(\Gamma_0(N)\)-optimal
840.j6 840j6 [0, 1, 0, 2400, 2400] [2] 1024  

Rank

sage: E.rank()
 

The elliptic curves in class 840.j have rank \(0\).

Modular form 840.2.a.j

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} - q^{7} + q^{9} + 4q^{11} - 2q^{13} + q^{15} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.