Properties

Label 266616.bf
Number of curves $2$
Conductor $266616$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("bf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 266616.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
266616.bf1 266616bf2 \([0, 0, 0, -2324955, 1364383046]\) \(12576878500/1127\) \(124542740267301888\) \([2]\) \(4055040\) \(2.3203\)  
266616.bf2 266616bf1 \([0, 0, 0, -134895, 24504338]\) \(-9826000/3703\) \(-102302965219569408\) \([2]\) \(2027520\) \(1.9737\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 266616.bf have rank \(1\).

Complex multiplication

The elliptic curves in class 266616.bf do not have complex multiplication.

Modular form 266616.2.a.bf

sage: E.q_eigenform(10)
 
\(q + q^{7} + 4q^{11} + 6q^{13} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.