Properties

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

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

Elliptic curves in class 69696.fu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
69696.fu1 69696gh4 \([0, 0, 0, -2057484, -1135779568]\) \(5690357426/891\) \(150824283062796288\) \([2]\) \(983040\) \(2.3072\)  
69696.fu2 69696gh2 \([0, 0, 0, -140844, -14161840]\) \(3650692/1089\) \(92170395205042176\) \([2, 2]\) \(491520\) \(1.9607\)  
69696.fu3 69696gh1 \([0, 0, 0, -53724, 4621232]\) \(810448/33\) \(698260569735168\) \([2]\) \(245760\) \(1.6141\) \(\Gamma_0(N)\)-optimal
69696.fu4 69696gh3 \([0, 0, 0, 381876, -94660720]\) \(36382894/43923\) \(-7435078546540068864\) \([2]\) \(983040\) \(2.3072\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 69696.fu do not have complex multiplication.

Modular form 69696.2.a.fu

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

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.