Properties

Label 259182.fu
Number of curves $4$
Conductor $259182$
CM no
Rank $0$
Graph

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

Elliptic curves in class 259182.fu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
259182.fu1 259182fu3 \([1, -1, 1, -5531054, 5008177221]\) \(14489843500598257/6246072\) \(8066601920067768\) \([2]\) \(8847360\) \(2.3948\)  
259182.fu2 259182fu4 \([1, -1, 1, -739454, -129184635]\) \(34623662831857/14438442312\) \(18646785768202304328\) \([2]\) \(8847360\) \(2.3948\)  
259182.fu3 259182fu2 \([1, -1, 1, -347414, 77498853]\) \(3590714269297/73410624\) \(94807469480302656\) \([2, 2]\) \(4423680\) \(2.0482\)  
259182.fu4 259182fu1 \([1, -1, 1, 1066, 3621093]\) \(103823/4386816\) \(-5665432349896704\) \([2]\) \(2211840\) \(1.7017\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 259182.fu have rank \(0\).

Complex multiplication

The elliptic curves in class 259182.fu do not have complex multiplication.

Modular form 259182.2.a.fu

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 2q^{5} + q^{7} + q^{8} + 2q^{10} + 6q^{13} + q^{14} + q^{16} + q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.