Properties

Label 69696.ea
Number of curves 4
Conductor 69696
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("69696.ea1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 69696.ea

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69696.ea1 69696fn3 [0, 0, 0, -5611980, 5097474448] [2] 2211840  
69696.ea2 69696fn4 [0, 0, 0, -2824140, 10163537296] [2] 4423680  
69696.ea3 69696fn1 [0, 0, 0, -384780, -86653424] [2] 737280 \(\Gamma_0(N)\)-optimal
69696.ea4 69696fn2 [0, 0, 0, 312180, -365716208] [2] 1474560  

Rank

sage: E.rank()
 

The elliptic curves in class 69696.ea have rank \(0\).

Modular form 69696.2.a.ea

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 LMFDB 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 LMFDB labels.