Properties

Label 69696bn
Number of curves 4
Conductor 69696
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("69696.df1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 69696bn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69696.df3 69696bn1 [0, 0, 0, -384780, 86653424] [2] 737280 \(\Gamma_0(N)\)-optimal
69696.df4 69696bn2 [0, 0, 0, 312180, 365716208] [2] 1474560  
69696.df1 69696bn3 [0, 0, 0, -5611980, -5097474448] [2] 2211840  
69696.df2 69696bn4 [0, 0, 0, -2824140, -10163537296] [2] 4423680  

Rank

sage: E.rank()
 

The elliptic curves in class 69696bn have rank \(1\).

Modular form 69696.2.a.df

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

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.