Properties

Label 7744.bf
Number of curves $2$
Conductor $7744$
CM no
Rank $1$
Graph

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

Elliptic curves in class 7744.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7744.bf1 7744bb2 [0, -1, 0, -232481, -43068991] [] 33792  
7744.bf2 7744bb1 [0, -1, 0, -161, 3137] [] 3072 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7744.bf have rank \(1\).

Complex multiplication

The elliptic curves in class 7744.bf do not have complex multiplication.

Modular form 7744.2.a.bf

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - q^{5} + 2q^{7} + q^{9} - q^{13} - 2q^{15} - 5q^{17} + 6q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.