Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("69696.fu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 69696.fu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69696.fu1 69696gh4 [0, 0, 0, -2057484, -1135779568] [2] 983040  
69696.fu2 69696gh2 [0, 0, 0, -140844, -14161840] [2, 2] 491520  
69696.fu3 69696gh1 [0, 0, 0, -53724, 4621232] [2] 245760 \(\Gamma_0(N)\)-optimal
69696.fu4 69696gh3 [0, 0, 0, 381876, -94660720] [2] 983040  

Rank

sage: E.rank()
 

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

Modular form 69696.2.a.fu

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.