Properties

Label 69696gj
Number of curves 2
Conductor 69696
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("69696.fj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 69696gj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69696.fj2 69696gj1 [0, 0, 0, 11616, 266200] [2] 184320 \(\Gamma_0(N)\)-optimal
69696.fj1 69696gj2 [0, 0, 0, -53724, 2278672] [2] 368640  

Rank

sage: E.rank()
 

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

Modular form 69696.2.a.fj

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

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.