Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7744bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7744.be2 7744bc1 [0, -1, 0, -1921, 33057] [] 3072 \(\Gamma_0(N)\)-optimal
7744.be1 7744bc2 [0, -1, 0, -19521, -4097311] [] 33792  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 7744.2.a.bc

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 Cremona 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 Cremona labels.