Properties

Label 840.d
Number of curves 6
Conductor 840
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("840.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 840.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
840.d1 840f5 [0, -1, 0, -10480, -409460] [2] 1024  
840.d2 840f3 [0, -1, 0, -680, -5700] [2, 2] 512  
840.d3 840f2 [0, -1, 0, -180, 900] [2, 4] 256  
840.d4 840f1 [0, -1, 0, -175, 952] [4] 128 \(\Gamma_0(N)\)-optimal
840.d5 840f4 [0, -1, 0, 240, 4092] [4] 512  
840.d6 840f6 [0, -1, 0, 1120, -32340] [2] 1024  

Rank

sage: E.rank()
 

The elliptic curves in class 840.d have rank \(1\).

Modular form 840.2.a.d

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.