Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("840.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 840.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
840.f1 840g5 [0, -1, 0, -24400, -1458548] [2] 2048  
840.f2 840g3 [0, -1, 0, -1720, -16100] [2, 2] 1024  
840.f3 840g2 [0, -1, 0, -740, 7812] [2, 4] 512  
840.f4 840g1 [0, -1, 0, -735, 7920] [4] 256 \(\Gamma_0(N)\)-optimal
840.f5 840g4 [0, -1, 0, 160, 24732] [4] 1024  
840.f6 840g6 [0, -1, 0, 5280, -119700] [2] 2048  

Rank

sage: E.rank()
 

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

Modular form 840.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{5} + q^{7} + q^{9} + 4q^{11} - 2q^{13} - q^{15} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.