Properties

Label 77616fk
Number of curves 6
Conductor 77616
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("77616.bf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 77616fk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
77616.bf4 77616fk1 [0, 0, 0, -240051, -45254734] [2] 491520 \(\Gamma_0(N)\)-optimal
77616.bf3 77616fk2 [0, 0, 0, -275331, -31079230] [2, 2] 983040  
77616.bf6 77616fk3 [0, 0, 0, 888909, -225041614] [2] 1966080  
77616.bf2 77616fk4 [0, 0, 0, -2004051, 1070115410] [2, 2] 1966080  
77616.bf5 77616fk5 [0, 0, 0, 218589, 3313648226] [2] 3932160  
77616.bf1 77616fk6 [0, 0, 0, -31886211, 69303039554] [2] 3932160  

Rank

sage: E.rank()
 

The elliptic curves in class 77616fk have rank \(0\).

Modular form 77616.2.a.bf

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.